5,084 results on '"Weak convergence"'
Search Results
2. New Results on the Quasilinearization Method for Time Scales.
- Author
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Çetin, Şahap, Yılmaz, Yalçın, and Yakar, Coşkun
- Subjects
- *
INITIAL value problems , *QUASILINEARIZATION , *TIME management , *EQUATIONS - Abstract
We have developed the generalized quasilinearization method (QM) for an initial value problem (IVP) of dynamic equations on time scales by using comparison theorems with a coupled lower solution (LS) and upper solution (US) of the natural type. Under some conditions, we observed that the solutions converged to the unique solution of the problem uniformly and monotonically, and the rate of convergence was investigated. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
3. A Joint Limit Theorem for Epstein and Hurwitz Zeta-Functions.
- Author
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Gerges, Hany, Laurinčikas, Antanas, and Macaitienė, Renata
- Subjects
- *
ZETA functions , *PROBABILITY measures , *LIMIT theorems , *HAAR integral - Abstract
In the paper, we prove a joint limit theorem in terms of the weak convergence of probability measures on C 2 defined by means of the Epstein ζ (s ; Q) and Hurwitz ζ (s , α) zeta-functions. The limit measure in the theorem is explicitly given. For this, some restrictions on the matrix Q and the parameter α are required. The theorem obtained extends and generalizes the Bohr-Jessen results characterising the asymptotic behaviour of the Riemann zeta-function. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
4. A recent proximal gradient algorithm for convex minimization problem using double inertial extrapolations.
- Author
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Suparat Kesornprom, Papatsara Inkrong, Uamporn Witthayarat, and Prasit Cholamjiak
- Subjects
EXTRAPOLATION ,IMAGE reconstruction ,FORWARD-backward algorithm ,ALGORITHMS ,CLASSIFICATION algorithms - Abstract
In this study, we suggest a new class of forward-backward (FB) algorithms designed to solve convex minimization problems. Our method incorporates a linesearch technique, eliminating the need to choose Lipschitz assumptions explicitly. Additionally, we apply double inertial extrapolations to enhance the algorithm’s convergence rate. We establish a weak convergence theorem under some mild conditions. Furthermore, we perform numerical tests, and apply the algorithm to image restoration and data classification as a practical application. The experimental results show our approach’s superior performance and effectiveness, surpassing some existing methods in the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
5. An Elementary Model of Focal Adhesion Detachment and Reattachment During Cell Reorientation Using Ideas from the Kinetics of Wiggly Energies.
- Author
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Abeyaratne, Rohan, Puntel, Eric, and Tomassetti, Giuseppe
- Subjects
FOCAL adhesions ,FIBER orientation ,ADHESION ,ACTIVATION energy ,STRETCH (Physiology) - Abstract
A simple, transparent, two-dimensional, nonlinear model of cell reorientation is constructed in this paper. The cells are attached to a substrate by "focal adhesions" that transmit the deformation of the substrate to the "stress fibers" in the cell. When the substrate is subjected to a deformation, say an in-plane bi-axial deformation with stretches λ 1 and λ 2 , the stress fibers deform with it and change their length and orientation. In addition, the focal adhesions can detach from the substrate and reattach to it at new nearby locations, and this process of detachment and reattachment can happen many times. In this scenario the (varying) fiber angle Θ in the reference configuration plays the role of an internal variable. In addition to the elastic energy of the stress fibers, the energy associated with the focal adhesions is accounted for by a wiggly energy ϵ a cos Θ / ϵ , 0 < ϵ ≪ 1 . Each local minimum of this energy corresponds to a particular configuration of the focal adhesions. The small amplitude ϵ a indicates that the energy barrier between two neighboring configurations is relatively small, and the small distance 2 π ϵ between the local minima indicates that a focal adhesion does not have to move very far before it reattaches. The evolution of this system is studied using a gradient flow kinetic law, which is homogenized for ϵ → 0 using results from weak convergence. The results determine (a) a region of the λ 1 , λ 2 -plane in which the (referential) fiber orientation remains stuck at the angle Θ and does not evolve, and (b) the evolution of the orientation when the stretches move out of this region as the fibers seek to minimize energy. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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6. Large deviations for stochastic predator–prey model with Lévy noise.
- Author
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Sridevi, C. S., Suvinthra, Murugan, and Balachandran, Krishnan
- Subjects
PREDATORY animals ,APPROXIMATION theory ,MATHEMATICAL equivalence ,UNIQUENESS (Mathematics) ,MATHEMATICAL models - Abstract
This paper discusses the large deviations for stochastic predator–prey model driven by multiplicative Lévy noise. Using Galerkin approximation, we initially prove the existence and uniqueness of solution. Due to the equivalence between Laplace principle and large deviation principle under a Polish space, the method of weak convergence has been followed in order to establish our results for this coupled system of equations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
7. On generalized shifts of the Mellin transform of the Riemann zeta-function
- Author
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Laurinčikas Antanas and Šiaučiūnas Darius
- Subjects
approximation of analytic functions ,limit theorem ,mellin transform ,riemann zeta-function ,weak convergence ,11m06 ,Mathematics ,QA1-939 - Abstract
In this article, we consider the asymptotic behaviour of the modified Mellin transform Z(s){\mathcal{Z}}\left(s), s=σ+its=\sigma +it, of the Riemann zeta-function using weak convergence of probability measures in the space of analytic functions defined by means of shifts Z(s+iφ(τ)){\mathcal{Z}}\left(s+i\varphi \left(\tau )), where φ(τ)\varphi \left(\tau ) is a real increasing to +∞+\infty differentiable function with monotonically decreasing derivative satisfying a certain estimate connected to the second moment of Z(s){\mathcal{Z}}\left(s). We prove in this case that the limit measure is concentrated at the point g0(s)≡0{g}_{0}\left(s)\equiv 0. This result is applied to the approximation of g0(s){g}_{0}\left(s) by shifts Z(s+iφ(τ)){\mathcal{Z}}\left(s+i\varphi \left(\tau )).
- Published
- 2024
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8. روش اکستراگرادیان زیرگرادیان لخت برای حل مسائل تعادل.
- Author
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مریم صفری and فریدون مرادلو
- Abstract
In this paper, combining the subgradient extragradient method with inertial method, we introduce a new iterative algorithm for solving equilibrium problems in real Hilbert spaces. Moreover, we present a new inertial self-adaptive scheme for solving variational inequalities in real Hilbert spaces, which it is not necessary to know the Lipschitz constant of the mapping. We prove the weak convergence of the generated iterates by presented algorithms. To illustrate the usability of our results and also to show the efficiency of the proposed methods, we present some comparative examples with several existing schemes in the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
9. Homogenization of the heat equation with random convolutional potential
- Author
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Mengmeng Wang, Dong Su, and Wei Wang
- Subjects
homogenization ,weak convergence ,random convolutional potential ,heat equation ,Mathematics ,QA1-939 - Abstract
This paper derived the homogenization of the heat equation with random convolutional potential. By Tartar's method of oscillating test function, the solution of the heat equation with random convolutional potential was shown to converge in distribution to the solution of the effective equation with determined convolutional potential.
- Published
- 2024
- Full Text
- View/download PDF
10. Uniform in number of neighbors consistency and weak convergence of kNN empirical conditional processes and kNN conditional U-processes involving functional mixing data
- Author
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Salim Bouzebda and Amel Nezzal
- Subjects
conditional $ u $-statistic ,functional data analysis ,functional regression ,kolmogorov's entropy ,small ball probability ,$ k $nn kernel-type estimators ,empirical processes ,$ u $-processes ,weak convergence ,vc-classes ,Mathematics ,QA1-939 - Abstract
$ U $-statistics represent a fundamental class of statistics arising from modeling quantities of interest defined by multi-subject responses. $ U $-statistics generalize the empirical mean of a random variable $ X $ to sums over every $ m $-tuple of distinct observations of $ X $. Stute [182] introduced a class of so-called conditional $ U $-statistics, which may be viewed as a generalization of the Nadaraya-Watson estimates of a regression function. Stute proved their strong pointwise consistency to: $ r^{(m)}(\varphi, \mathbf{t}): = \mathbb{E}[\varphi(Y_{1}, \ldots, Y_{m})|(X_{1}, \ldots, X_{m}) = \mathbf{t}], \; \mbox{for}\; \mathbf{ t}\in \mathcal{X}^{m}. $ In this paper, we are mainly interested in the study of the $ k $NN conditional $ U $-processes in a functional mixing data framework. More precisely, we investigate the weak convergence of the conditional empirical process indexed by a suitable class of functions and of the $ k $NN conditional $ U $-processes when the explicative variable is functional. We treat the uniform central limit theorem in both cases when the class of functions is bounded or unbounded satisfying some moment conditions. The second main contribution of this study is the establishment of a sharp almost complete Uniform consistency in the Number of Neighbors of the constructed estimator. Such a result allows the number of neighbors to vary within a complete range for which the estimator is consistent. Consequently, it represents an interesting guideline in practice to select the optimal bandwidth in nonparametric functional data analysis. These results are proved under some standard structural conditions on the Vapnik-Chervonenkis classes of functions and some mild conditions on the model. The theoretical results established in this paper are (or will be) key tools for further functional data analysis developments. Potential applications include the set indexed conditional U-statistics, Kendall rank correlation coefficient, the discrimination problems and the time series prediction from a continuous set of past values.
- Published
- 2024
- Full Text
- View/download PDF
11. Large-Scale Block Bundle Adjustment of LROC NAC Images for Lunar South Pole Mapping Based on Topographic Constraint
- Author
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Chen Chen, Zhen Ye, Yusheng Xu, Dayong Liu, Rong Huang, Miyu Zhou, Huan Xie, and Xiaohua Tong
- Subjects
Large-scale bundle block adjustment (BBA) ,lunar south pole ,outlier elimination ,topographic constraint ,weak convergence ,Ocean engineering ,TC1501-1800 ,Geophysics. Cosmic physics ,QC801-809 - Abstract
With the increasing interest in the south polar region of the Moon, there is an urgent need for high-resolution mapping products to support future exploration. Bundle block adjustment (BBA) is able to improve the spatial positioning accuracy of images used to generate high-precision mapping products. However, the impacts of weak-convergence geometry and poor illumination conditions in lunar south pole on BBA still need to be solved. This article proposes a large-scale robust BBA method for narrow angle camera (NAC) images in south pole. The NAC images are taken from the Lunar Reconnaissance Orbiter, which are scanner-type images requiring special treatment beyond the classical BBA of framing camera images. To handle the weak-convergence geometry issue of stereo NAC imagery, a topographic constraint using reference digital elevation model is integrated into BBA with an appropriate weighting scheme to estimate local topographic relief. In addition, a two-stage outlier elimination strategy for BBA with absolute-relative thresholding and iteratively reweighting methods is presented to reject outliers caused by the poor illumination conditions in lunar south pole. Thousands of images are used for experimental tests and lunar orbiter laser altimeter digital elevation models (DEMs) with different resolutions are used as reference data. The satisfactory experimental results demonstrate the effectiveness and reliability of our BBA method. The proposed large-scale BBA method reduces the relative positioning errors in block network to within 1 m, and decreases the inconsistency between NAC images caused by the orientation errors to less than 0.5 pixel, which offers a reliable solution for large-scale controlled mapping.
- Published
- 2024
- Full Text
- View/download PDF
12. On Universality of Some Beurling Zeta-Functions.
- Author
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Geštautas, Andrius and Laurinčikas, Antanas
- Subjects
- *
ANALYTIC functions , *DIRICHLET series , *ZETA functions , *AXIOMS , *HAAR integral , *INTEGERS , *RIEMANN hypothesis - Abstract
Let P be the set of generalized prime numbers, and ζ P (s) , s = σ + i t , denote the Beurling zeta-function associated with P. In the paper, we consider the approximation of analytic functions by using shifts ζ P (s + i τ) , τ ∈ R . We assume the classical axioms for the number of generalized integers and the mean of the generalized von Mangoldt function, the linear independence of the set { log p : p ∈ P } , and the existence of a bounded mean square for ζ P (s) . Under the above hypotheses, we obtain the universality of the function ζ P (s) . This means that the set of shifts ζ P (s + i τ) approximating a given analytic function defined on a certain strip σ ^ < σ < 1 has a positive lower density. This result opens a new chapter in the theory of Beurling zeta functions. Moreover, it supports the Linnik–Ibragimov conjecture on the universality of Dirichlet series. For the proof, a probabilistic approach is applied. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
13. Homogenization of the heat equation with random convolutional potential.
- Author
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Wang, Mengmeng, Su, Dong, and Wang, Wei
- Subjects
HEAT equation ,ASYMPTOTIC homogenization ,TATARS - Abstract
This paper derived the homogenization of the heat equation with random convolutional potential. By Tartar's method of oscillating test function, the solution of the heat equation with random convolutional potential was shown to converge in distribution to the solution of the effective equation with determined convolutional potential. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
14. Uniform in number of neighbors consistency and weak convergence of kNN empirical conditional processes and kNN conditional U-processes involving functional mixing data.
- Author
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Bouzebda, Salim and Nezzal, Amel
- Subjects
EMPIRICAL research ,RANK correlation (Statistics) ,CENTRAL limit theorem ,U-statistics ,RANDOM variables ,QUANTILE regression ,FUNCTIONAL analysis ,INDEPENDENT variables - Abstract
U-statistics represent a fundamental class of statistics arising from modeling quantities of interest defined by multi-subject responses. U-statistics generalize the empirical mean of a random variable X to sums over every m-tuple of distinct observations of X. Stute [182] introduced a class of so-called conditional U-statistics, which may be viewed as a generalization of the Nadaraya-Watson estimates of a regression function. Stute proved their strong pointwise consistency to: r
(m) (φ, t) ≔ 피[φ(F1 ,..., Ym )|(X1 ,..., Xm ) = t], for t ∈ Xm . In this paper, we are mainly interested in the study of the kNN conditional U-processes in a functional mixing data framework. More precisely, we investigate the weak convergence of the conditional empirical process indexed by a suitable class of functions and of the kNN conditional U-processes when the explicative variable is functional. We treat the uniform central limit theorem in both cases when the class of functions is bounded or unbounded satisfying some moment conditions. The second main contribution of this study is the establishment of a sharp almost complete Uniform consistency in the Number of Neighbors of the constructed estimator. Such a result allows the number of neighbors to vary within a complete range for which the estimator is consistent. Consequently, it represents an interesting guideline in practice to select the optimal bandwidth in nonparametric functional data analysis. These results are proved under some standard structural conditions on the Vapnik-Chervonenkis classes of functions and some mild conditions on the model. The theoretical results established in this paper are (or will be) key tools for further functional data analysis developments. Potential applications include the set indexed conditional U-statistics, Kendall rank correlation coefficient, the discrimination problems and the time series prediction from a continuous set of past values. [ABSTRACT FROM AUTHOR]- Published
- 2024
- Full Text
- View/download PDF
15. WEAK CONVERGENCE OF FIXED POINT ITERATIONS IN S-METRIC SPACES.
- Author
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SIVA, G. and LOGANATHAN, S.
- Subjects
FIXED point theory ,MATHEMATICAL inequalities ,ALGORITHMS ,MATHEMATICAL models ,MACHINE learning - Abstract
This paper extends the notion of weak convergence in metric spaces to the case of S-metric spaces. Moreover, some results on the weak convergence of fixed point iterations of Banach’s, Kannan’s, Chatterjea’s, Reich’s, Hardy and Roger’s types of contractions on S-metric spaces are obtained. In addition, an example is presented to demonstrate our primary result. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
16. Noncentral moderate deviations for fractional Skellam processes.
- Author
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Jeonghwa Lee and Macci, Claudio
- Subjects
POISSON processes ,LARGE deviations (Mathematics) ,WIENER processes ,GAUSSIAN distribution ,DEVIATION (Statistics) - Abstract
The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability to zero (governed by a large deviation principle) and a weak convergence to a centered Normal distribution. The notion of noncentral moderate deviations is used when the weak convergence is towards a non-Gaussian distribution. In this paper, noncentral moderate deviation results are presented for two fractional Skellam processes known in the literature (see [20]). It is established that, for the fractional Skellam process of type 2 (for which one can refer to the recent results for compound fractional Poisson processes in [3]), the convergences to zero are usually faster because one can prove suitable inequalities between rate functions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
17. Large deviations for stochastic predator–prey model with Lévy noise
- Author
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C.S. Sridevi, Murugan Suvinthra, and Krishnan Balachandran
- Subjects
large deviation principle ,predator–prey model ,weak convergence ,Lévy noise ,Analysis ,QA299.6-433 - Abstract
This paper discusses the large deviations for stochastic predator–prey model driven by multiplicative Lévy noise. Using Galerkin approximation, we initially prove the existence and uniqueness of solution. Due to the equivalence between Laplace principle and large deviation principle under a Polish space, the method of weak convergence has been followed in order to establish our results for this coupled system of equations.
- Published
- 2024
- Full Text
- View/download PDF
18. Homogenization of Attractors to Ginzburg-Landau Equations in Media with Locally Periodic Obstacles: Sub- and Supercritical Cases
- Author
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K.A. Бекмаганбетов, Г.А. Чечкин, В.В. Чепыжов, and A.А. Толемис
- Subjects
attractors ,homogenization ,Ginzburg-Landau equations ,nonlinear equations ,weak convergence ,perforated domain ,Analysis ,QA299.6-433 ,Analytic mechanics ,QA801-939 ,Probabilities. Mathematical statistics ,QA273-280 - Abstract
The Ginzburg-Landau equation with rapidly oscillating terms in the equation and boundary conditions in a perforated domain was considered. Proof was given that the trajectory attractors of this equation converge weakly to the trajectory attractors of the homogenized Ginzburg-Landau equation. To do this, we use the approach from the articles and monographs of V.V. Chepyzhov and M.I. Vishik about trajectory attractors of evolutionary equations, and we also use homogenization methods that appeared at the end of the 20th century. First, we use asymptotic methods to construct asymptotics formally, and then we justify the form of the main terms of the asymptotic series using functional analysis and integral estimates. By defining the corresponding auxiliary function spaces with weak topology, we derive a limit (homogenized) equation and prove the existence of a trajectory attractor for this equation. Then, we formulate the main theorems and prove them by using auxiliary lemmas. We prove that the trajectory attractors of this equation tend in a weak sense to the trajectory attractors of the homogenized Ginzburg-Landau equation in the subcritical case, and they disappear in the supercritical case.
- Published
- 2024
- Full Text
- View/download PDF
19. Noncentral moderate deviations for fractional Skellam processes
- Author
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Jeonghwa Lee and Claudio Macci
- Subjects
Mittag-Leffler function ,inverse of stable subordinator ,weak convergence ,Applied mathematics. Quantitative methods ,T57-57.97 ,Mathematics ,QA1-939 - Abstract
The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability to zero (governed by a large deviation principle) and a weak convergence to a centered Normal distribution. The notion of noncentral moderate deviations is used when the weak convergence is towards a non-Gaussian distribution. In this paper, noncentral moderate deviation results are presented for two fractional Skellam processes known in the literature (see [20]). It is established that, for the fractional Skellam process of type 2 (for which one can refer to the recent results for compound fractional Poisson processes in [3]), the convergences to zero are usually faster because one can prove suitable inequalities between rate functions.
- Published
- 2023
- Full Text
- View/download PDF
20. Weak convergence of fixed point iterations in $S$-metric spaces
- Author
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Siva G and Loganathan S
- Subjects
weak convergence ,semi s-metric space ,directed set ,Mathematics ,QA1-939 - Abstract
This paper extends the notion of weak convergence in metric spaces to the case of S-metric spaces. Moreover, some results on the weak convergence of fixed point iterations of Banach's, Kannan's, Chatterjee's, Reich's, Hardy and Roger's types of contractions on S-metric spaces are obtained. In addition, an example is presented to demonstrate our primary result.
- Published
- 2023
- Full Text
- View/download PDF
21. A faster iterative scheme for solving nonlinear fractional differential equations of the Caputo type
- Author
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Godwin Amechi Okeke, Akanimo Victor Udo, Rubayyi T. Alqahtani, and Nadiyah Hussain Alharthi
- Subjects
fixed point ,rate of convergence ,ag iterative scheme ,caputo fractional differential equation ,weak convergence ,$ \mathcal{j} $-stability ,Mathematics ,QA1-939 - Abstract
In this paper, we introduce a new fixed point iterative scheme called the AG iterative scheme that is used to approximate the fixed point of a contraction mapping in a uniformly convex Banach space. The iterative scheme is used to prove some convergence result. The stability of the new scheme is shown. Furthermore, weak convergence of Suzuki's generalized non-expansive mapping satisfying condition (C) is shown. The rate of convergence result is proved and it is demonstrated via an illustrative example which shows that our iterative scheme converges faster than the Picard, Mann, Noor, Picard-Mann, M and Thakur iterative schemes. Data dependence results for the iterative scheme are shown. Finally, our result is used to approximate the solution of a nonlinear fractional differential equation of Caputo type.
- Published
- 2023
- Full Text
- View/download PDF
22. New inertial self-adaptive algorithms for the split common null-point problem: application to data classifications
- Author
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Ratthaprom Promkam, Pongsakorn Sunthrayuth, Suparat Kesornprom, and Ekapak Tanprayoon
- Subjects
p-uniformly convex Banach spaces ,Weak convergence ,Split common null-point problem ,Maximal monotone operator ,Self-adaptive algorithm ,Mathematics ,QA1-939 - Abstract
Abstract In this paper, we propose two inertial algorithms with a new self-adaptive step size for approximating a solution of the split common null-point problem in the framework of Banach spaces. The step sizes are adaptively updated over each iteration by a simple process without the prior knowledge of the operator norm of the bounded linear operator. Under suitable conditions, we prove the weak-convergence results for the proposed algorithms in p-uniformly convex and uniformly smooth Banach spaces. Finally, we give several numerical results in both finite- and infinite-dimensional spaces to illustrate the efficiency and advantage of the proposed methods over some existing methods. Also, data classifications of heart diseases and diabetes mellitus are presented as the applications of our methods.
- Published
- 2023
- Full Text
- View/download PDF
23. Remarks on the Connection of the Riemann Hypothesis to Self-Approximation
- Author
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Antanas Laurinčikas
- Subjects
Riemann hypothesis ,Riemann zeta-function ,universality ,weak convergence ,Electronic computers. Computer science ,QA75.5-76.95 - Abstract
By the Bagchi theorem, the Riemann hypothesis (all non-trivial zeros lie on the critical line) is equivalent to the self-approximation of the function ζ(s) by shifts ζ(s+iτ). In this paper, it is determined that the Riemann hypothesis is equivalent to the positivity of density of the set of the above shifts approximating ζ(s) with all but at most countably many accuracies ε>0. Also, the analogue of an equivalent in terms of positive density in short intervals is discussed.
- Published
- 2024
- Full Text
- View/download PDF
24. New Results on the Quasilinearization Method for Time Scales
- Author
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Şahap Çetin, Yalçın Yılmaz, and Coşkun Yakar
- Subjects
quasilinearization ,quadratic convergence ,weak convergence ,extremal solutions ,time scale ,Mathematics ,QA1-939 - Abstract
We have developed the generalized quasilinearization method (QM) for an initial value problem (IVP) of dynamic equations on time scales by using comparison theorems with a coupled lower solution (LS) and upper solution (US) of the natural type. Under some conditions, we observed that the solutions converged to the unique solution of the problem uniformly and monotonically, and the rate of convergence was investigated.
- Published
- 2024
- Full Text
- View/download PDF
25. Large deviations for the two-time-scale stochastic convective Brinkman-Forchheimer equations.
- Author
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Mohan, Manil T.
- Subjects
- *
LARGE deviations (Mathematics) , *STOCHASTIC partial differential equations , *REACTION-diffusion equations , *EQUATIONS , *RANDOM noise theory - Abstract
The convective Brinkman-Forchheimer (CBF) equations are employed to characterize the motion of incompressible fluid in a saturated porous medium. This work investigates the small noise asymptotic of two-time-scale stochastic CBF equations in two and three dimensional bounded domains. More precisely, we establish a Wentzell-Freidlin type large deviation principle for stochastic partial differential equations that have slow and fast time-scales. The slow component is the stochastic CBF equations in two or three dimensions perturbed by a small multiplicative Gaussian noise, while the fast component is a stochastic reaction-diffusion equation with damping. The results are obtained by using a variational method (based on weak convergence approach) developed by Budhiraja and Dupuis, Khasminkii's time discretization approach and stopping time arguments. In particular, the findings from this study are also applicable to two-dimensional stochastic Navier-Stokes equations. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
26. A faster iterative scheme for solving nonlinear fractional differential equations of the Caputo type.
- Author
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Okeke, Godwin Amechi, Udo, Akanimo Victor, Alqahtani, Rubayyi T., and Alharthi, Nadiyah Hussain
- Subjects
NONLINEAR differential equations ,NONEXPANSIVE mappings ,BANACH spaces ,FRACTIONAL differential equations - Abstract
In this paper, we introduce a new fixed point iterative scheme called the AG iterative scheme that is used to approximate the fixed point of a contraction mapping in a uniformly convex Banach space. The iterative scheme is used to prove some convergence result. The stability of the new scheme is shown. Furthermore, weak convergence of Suzuki's generalized non-expansive mapping satisfying condition (C) is shown. The rate of convergence result is proved and it is demonstrated via an illustrative example which shows that our iterative scheme converges faster than the Picard, Mann, Noor, Picard-Mann, M and Thakur iterative schemes. Data dependence results for the iterative scheme are shown. Finally, our result is used to approximate the solution of a nonlinear fractional differential equation of Caputo type. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
27. Gram Points in the Universality of the Dirichlet Series with Periodic Coefficients.
- Author
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Šiaučiūnas, Darius and Tekorė, Monika
- Subjects
- *
DIRICHLET series , *ANALYTIC functions , *ANALYTIC spaces , *COMPLEX numbers , *PROBABILITY measures - Abstract
Let a = { a m : m ∈ N } be a periodic multiplicative sequence of complex numbers and L (s ; a) , s = σ + i t a Dirichlet series with coefficients a m . In the paper, we obtain a theorem on the approximation of non-vanishing analytic functions defined in the strip 1 / 2 < σ < 1 via discrete shifts L (s + i h t k ; a) , h > 0 , k ∈ N , where { t k : k ∈ N } is the sequence of Gram points. We prove that the set of such shifts approximating a given analytic function is infinite. This result extends and covers that of [Korolev, M.; Laurinčikas, A. A new application of the Gram points. Aequat. Math. 2019, 93, 859–873]. For the proof, a limit theorem on weakly convergent probability measures in the space of analytic functions is applied. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
28. A Quicker Iteration Method for Approximating the Fixed Point of Generalized α -Reich-Suzuki Nonexpansive Mappings with Applications.
- Author
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Ali, Danish, Ali, Shahbaz, Pompei-Cosmin, Darab, Antoniu, Turcu, Zaagan, Abdullah A., and Mahnashi, Ali M.
- Subjects
- *
NONEXPANSIVE mappings , *FIXED point theory , *BANACH spaces , *COMPUTER science - Abstract
Fixed point theory is a branch of mathematics that studies solutions that remain unchanged under a given transformation or operator, and it has numerous applications in fields such as mathematics, economics, computer science, engineering, and physics. In the present article, we offer a quicker iteration technique, the D * * iteration technique, for approximating fixed points in generalized α -nonexpansive mappings and nearly contracted mappings. In uniformly convex Banach spaces, we develop weak and strong convergence results for the D * * iteration approach to the fixed points of generalized α -nonexpansive mappings. In order to demonstrate the effectiveness of our recommended iteration strategy, we provide comprehensive analytical, numerical, and graphical explanations. Here, we also demonstrate the stability consequences of the new iteration technique. We approximately solve a fractional Volterra–Fredholm integro-differential problem as an application of our major findings. Our findings amend and expand upon some previously published results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
29. NEW BREGMAN PROJECTION ALGORITHMS FOR SOLVING THE SPLIT FEASIBILITY PROBLEM.
- Author
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YAXIN HAO and JING ZHAO
- Subjects
FEASIBILITY problem (Mathematical optimization) ,ITERATIVE methods (Mathematics) ,SIGNAL processing ,STOCHASTIC convergence ,PROBLEM solving - Abstract
Bregman distance iterative methods for solving optimization problems are important and interesting because of the numerous applications of Bregman distance techniques. In this paper, for solving a split feasibility problem, we introduce a new Bregman projection algorithm and construct two selection strategies of stepsizes. Moreover, a relaxed Bregman projection algorithm is proposed with two selection strategies of stepsizes, where the two closed and convex sets are both level sets of convex functions. Weak convergence results of the proposed algorithms are obtained under suitable assumptions. In addition, using the proposed algorithms with different Bregman distances, a numerical experiment solving signal processing problem is also given to demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
30. New inertial self-adaptive algorithms for the split common null-point problem: application to data classifications.
- Author
-
Promkam, Ratthaprom, Sunthrayuth, Pongsakorn, Kesornprom, Suparat, and Tanprayoon, Ekapak
- Subjects
- *
BANACH spaces , *SELF-adaptive software , *NOSOLOGY , *ALGORITHMS , *HEART diseases , *MONOTONE operators - Abstract
In this paper, we propose two inertial algorithms with a new self-adaptive step size for approximating a solution of the split common null-point problem in the framework of Banach spaces. The step sizes are adaptively updated over each iteration by a simple process without the prior knowledge of the operator norm of the bounded linear operator. Under suitable conditions, we prove the weak-convergence results for the proposed algorithms in p-uniformly convex and uniformly smooth Banach spaces. Finally, we give several numerical results in both finite- and infinite-dimensional spaces to illustrate the efficiency and advantage of the proposed methods over some existing methods. Also, data classifications of heart diseases and diabetes mellitus are presented as the applications of our methods. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
31. Gibbs Distribution and the Repairman Problem.
- Author
-
Chetouani, Hassan and Limnios, Nikolaos
- Subjects
- *
BOLTZMANN factor , *LYAPUNOV functions , *CALCULUS - Abstract
In this paper, we obtain weak convergence results for a family of Gibbs measures depending on the parameter θ > 0 in the following form d P θ (x) = Z θ exp − H θ (x) / θ d Q (x) , where we show that the limit distribution is concentrated in the set of the global minima of the limit Gibbs potential. We also give an explicit calculus for the limit distribution. Here, we use the above as an alternative to Lyapunov's function or to direct methods for stationary probability convergence and apply it to the repairman problem. Finally, we illustrate this method with a numerical example. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
32. On Joint Discrete Universality of the Riemann Zeta-Function in Short Intervals.
- Author
-
Chakraborty, Kalyan, Kanemitsu, Shigeru, and Laurinčikas, Antanas
- Subjects
- *
ALGEBRAIC numbers , *DIRICHLET series , *ZETA functions , *ANALYTIC functions - Abstract
In the paper, we prove that the set of discrete shifts of the Riemann zeta-function (ζ(s + 2πia1k), . . ., ζ(s + 2πiark)), k ∈ N, approximating analytic non-vanishing functions f1(s), . . ., fr(s) defined on {s ∈ C : 1/2 < Res < 1} has a positive density in the interval [N,N + M] with M = o(N), N → ∞, with real algebraic numbers a1, . . ., ar linearly independent over Q. A similar result is obtained for shifts of certain absolutely convergent Dirichlet series. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
33. New extrapolation projection contraction algorithms based on the golden ratio for pseudo-monotone variational inequalities.
- Author
-
Cuijie Zhang and Zhaoyang Chu
- Subjects
GOLDEN ratio ,EXTRAPOLATION ,VARIATIONAL inequalities (Mathematics) ,ALGORITHMS ,HILBERT space - Abstract
In real Hilbert spaces, for the purpose of trying to deal with the pseudo-monotone variational inequalities problem, we present a new extrapolation projection contraction algorithm based on the golden ratio in this study. Unlike ordinary inertial extrapolation, the algorithms are constructed based on a convex combined structure about the entire iterative trajectory. Extrapolation parameter ϕ is selected in a more relaxed range instead of only taking the golden ratio ϕ = √5+1/2 as the upper bound. Second, we propose an alternating extrapolation projection contraction algorithm to better increase the convergence effects of the extrapolation projection contraction algorithm based on the golden ratio. All our algorithms employ non-constantly decreasing adaptive step-sizes. The weak convergence results of the two algorithms are established for the pseudo-monotone variational inequalities. Additionally, the R-linear convergence results are investigated for strongly pseudo-monotone variational inequalities. Finally, we show the validity and superiority of the suggested methods with several numerical experiments. The numerical results show that alternating extrapolation does have obvious acceleration effect in practical application compared with no alternating extrapolation. Thus, the obvious effect of relaxing the selection range of parameter on our two algorithms is clearly demonstrated. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
34. On a new approach of enriched operators
- Author
-
Teodor Turcanu and Mihai Postolache
- Subjects
Generalized contraction ,Generalized nonexpansive mapping ,Mann iteration ,Weak convergence ,Strong convergence ,Science (General) ,Q1-390 ,Social sciences (General) ,H1-99 - Abstract
We establish the existence and uniqueness of fixed points of generalized contractions in the setting of Banach spaces and prove the convergence of Mann iteration for this general class of mappings. Also, we show the existence of fixed points and the convergence of Mann iteration as well for generalized nonexpansive mappings. Last but not least, we provide two applications, one from the field of numerical analysis of linear systems and another one dealing with functional equations. This new approach significantly extends the classes of enriched contractions and enriched nonexpansive mappings, and allows the use of Mann iteration as opposed to all papers on the subject, which necessarily have to rely on Krasnoselskij iteration.
- Published
- 2024
- Full Text
- View/download PDF
35. On the convergence, stability and data dependence results of the JK iteration process in Banach spaces
- Author
-
Ullah Kifayat, Saleem Naeem, Bilal Hazrat, Ahmad Junaid, Ibrar Muhammad, and Jarad Fahd
- Subjects
jk- iteration ,garcia-falset map ,strong convergence ,weak convergence ,data dependence ,stability ,banach space ,47h09 ,47h10 ,Mathematics ,QA1-939 - Abstract
This article analyzes the JK iteration process with the class of mappings that are essentially endowed with a condition called condition (E). The convergence of the iteration toward a fixed point of a specific mapping satisfying the condition (E) is obtained under some possible mild assumptions. It is worth mentioning that the iteration process JK converges better toward a fixed point compared to some prominent iteration processes in the literature. This fact is confirmed by a numerical example. Furthermore, it has been shown that the iterative scheme JK is stable in the setting of generalized contraction. The data dependence result is also established. Our results are new in the iteration theory and extend some recently announced results of the literature.
- Published
- 2023
- Full Text
- View/download PDF
36. A Joint Limit Theorem for Epstein and Hurwitz Zeta-Functions
- Author
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Hany Gerges, Antanas Laurinčikas, and Renata Macaitienė
- Subjects
Dirichlet L-function ,Epstein zeta-function ,Hurwitz zeta-function ,limit theorem ,Haar probability measure ,weak convergence ,Mathematics ,QA1-939 - Abstract
In the paper, we prove a joint limit theorem in terms of the weak convergence of probability measures on C2 defined by means of the Epstein ζ(s;Q) and Hurwitz ζ(s,α) zeta-functions. The limit measure in the theorem is explicitly given. For this, some restrictions on the matrix Q and the parameter α are required. The theorem obtained extends and generalizes the Bohr-Jessen results characterising the asymptotic behaviour of the Riemann zeta-function.
- Published
- 2024
- Full Text
- View/download PDF
37. Heart disease detection using inertial Mann relaxed CQ algorithms for split feasibility problems
- Author
-
Suthep Suantai, Pronpat Peeyada, Andreea Fulga, and Watcharaporn Cholamjiak
- Subjects
weak convergence ,inertial technique ,split feasibility problem ,data classification ,heart disease data ,Mathematics ,QA1-939 - Abstract
This study investigates the weak convergence of the sequences generated by the inertial relaxed $ CQ $ algorithm with Mann's iteration for solving the split feasibility problem in real Hilbert spaces. Moreover, we present the advantage of our algorithm by choosing a wider range of parameters than the recent methods. Finally, we apply our algorithm to solve the classification problem using the heart disease dataset collected from the UCI machine learning repository as a training set. The result shows that our algorithm performs better than many machine learning methods and also extreme learning machine with fast iterative shrinkage-thresholding algorithm (FISTA) and inertial relaxed $ CQ $ algorithm (IRCQA) under consideration according to accuracy, precision, recall, and F1-score.
- Published
- 2023
- Full Text
- View/download PDF
38. Inertial Iterative Algorithms for Split Variational Inclusion and Fixed Point Problems.
- Author
-
Filali, Doaa, Dilshad, Mohammad, Alyasi, Lujain Saud Muaydhid, and Akram, Mohammad
- Subjects
- *
ALGORITHMS , *NONEXPANSIVE mappings , *LINEAR operators , *HILBERT space - Abstract
This paper aims to present two inertial iterative algorithms for estimating the solution of split variational inclusion (S p VI s P) and its extended version for estimating the common solution of (S p VI s P) and fixed point problem (FPP) of a nonexpansive mapping in the setting of real Hilbert spaces. We establish the weak convergence of the proposed algorithms and strong convergence of the extended version without using the pre-estimated norm of a bounded linear operator. We also exhibit the reliability and behavior of the proposed algorithms using appropriate assumptions in a numerical example. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
39. Robustness Against Conflicting Prior Information in Regression.
- Author
-
Gagnon, Philippe
- Subjects
ROBUST statistics ,REGRESSION analysis ,CONFLICT management ,DATA analysis ,NUMERICAL analysis - Abstract
Including prior information about model parameters is a fundamental step of any Bayesian statistical analysis. It is viewed positively by some as it allows, among others, to quantitatively incorporate expert opinion about model parameters. It is viewed negatively by others because it sets the stage for subjectivity in statistical analysis. Certainly, it creates problems when the inference is skewed due to a conflict with the data collected. According to the theory of conflict resolution (O'Hagan and Pericchi, 2012), a solution to such problems is to diminish the impact of conflicting prior information, yielding inference consistent with the data. This is typically achieved by using heavy-tailed priors. We study both theoretically and numerically the efficacy of such a solution in a regression framework where the prior information about the coefficients takes the form of a product of density functions with known location and scale parameters. We study functions with regularly-varying tails (Student distributions), log-regularly-varying tails (as introduced in Desgagn'e (2015)), and propose functions with slower tail decays that allow to resolve any conflict that can happen under that regression framework, contrarily to the two previous types of functions. The code to reproduce all numerical experiments is available online. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
40. On Approximation by an Absolutely Convergent Integral Related to the Mellin Transform.
- Author
-
Laurinčikas, Antanas
- Subjects
- *
MELLIN transform , *ZETA functions , *INTEGRAL transforms , *ANALYTIC functions , *INTEGRALS - Abstract
In this paper, we consider the modified Mellin transform of the product of the square of the Riemann zeta function and the exponentially decreasing function, and we discuss its probabilistic and approximation properties. It turns out that this Mellin transform approximates the identical zero in the strip { s ∈ C : 1 / 2 < σ < 1 } . [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
41. Heart disease detection using inertial Mann relaxed $ CQ $ algorithms for split feasibility problems.
- Author
-
Suantai, Suthep, Peeyada, Pronpat, Fulga, Andreea, and Cholamjiak, Watcharaporn
- Subjects
HEART diseases ,MACHINE learning ,HILBERT space ,CLASSIFICATION algorithms ,ALGORITHMS ,THRESHOLDING algorithms - Abstract
This study investigates the weak convergence of the sequences generated by the inertial relaxed [Math Processing Error] C Q algorithm with Mann's iteration for solving the split feasibility problem in real Hilbert spaces. Moreover, we present the advantage of our algorithm by choosing a wider range of parameters than the recent methods. Finally, we apply our algorithm to solve the classification problem using the heart disease dataset collected from the UCI machine learning repository as a training set. The result shows that our algorithm performs better than many machine learning methods and also extreme learning machine with fast iterative shrinkage-thresholding algorithm (FISTA) and inertial relaxed [Math Processing Error] C Q algorithm (IRCQA) under consideration according to accuracy, precision, recall, and F1-score. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
42. On joint discrete universality of the Riemann zeta-function in short intervals
- Author
-
Kalyan Chakraborty, Shigeru Kanemitsu, and Antanas Laurinčikas
- Subjects
Riemann zeta-function ,universality ,weak convergence ,Mathematics ,QA1-939 - Abstract
In the paper, we prove that the set of discrete shifts of the Riemann zeta-function approximating analytic nonvanishing functions f1(s),...,fr(s) defined on has a positive density in the interval [N,N + M] with with real algebraic numbers a1,...,ar linearly independent over Q. A similar result is obtained for shifts of certain absolutely convergent Dirichlet series.
- Published
- 2023
- Full Text
- View/download PDF
43. An innovative inertial extra-proximal gradient algorithm for solving convex optimization problems with application to image and signal processing
- Author
-
Joshua Olilima, Adesanmi Mogbademu, M. Asif Memon, Adebowale Martins Obalalu, Hudson Akewe, and Jamel Seidu
- Subjects
Forward-backward algorithm ,Signal & image processing ,Convex minimization problem ,Weak convergence ,Inertial method ,Science (General) ,Q1-390 ,Social sciences (General) ,H1-99 - Abstract
This study introduces an innovative approach to address convex optimization problems, with a specific focus on applications in image and signal processing. The research aims to develop a self-adaptive extra proximal algorithm that incorporates an inertial term to effectively tackle challenges in convex optimization. The study's significance lies in its contribution to advancing optimization techniques in the realm of image deblurring and signal reconstruction. The proposed methodology involves creating a novel self-adaptive extra proximal algorithm, analyzing its convergence rigorously to ensure reliability and effectiveness. Numerical examples, including image deblurring and signal reconstruction tasks using only 10% of the original signal, illustrate the practical applicability and advantages of the algorithm. By introducing an inertial term within the extra proximal framework, the algorithm demonstrates potential for faster convergence and improved optimization outcomes, addressing real-world challenges of image enhancement and signal reconstruction. The algorithm's incorporation of an inertial term showcases its potential for faster convergence and improved optimization outcomes. This research significantly contributes to the field of optimization techniques, particularly in the context of image and signal processing applications.
- Published
- 2023
- Full Text
- View/download PDF
44. Joint Discrete Universality in the Selberg–Steuding Class.
- Author
-
Kačinskaitė, Roma, Laurinčikas, Antanas, and Žemaitienė, Brigita
- Subjects
- *
ANALYTIC functions , *ANALYTIC spaces , *PROBABILITY measures , *FUNCTION spaces , *LINEAR dependence (Mathematics) , *L-functions - Abstract
In the paper, we consider the approximation of analytic functions by shifts from the wide class S ˜ of L-functions. This class was introduced by A. Selberg, supplemented by J. Steuding, and is defined axiomatically. We prove the so-called joint discrete universality theorem for the function L (s) ∈ S ˜ . Using the linear independence over Q of the multiset (h j log p : p ∈ P) , j = 1 , ... , r ; 2 π for positive h j , we obtain that there are many infinite shifts L (s + i k h 1) , ... , L (s + i k h r) , k = 0 , 1 , ... , approximating every collection f 1 (s) , ... , f r (s) of analytic non-vanishing functions defined in the strip { s ∈ C : σ L < σ < 1 } , where σ L is a degree of the function L (s) . For the proof, the probabilistic approach based on weak convergence of probability measures in the space of analytic functions is applied. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
45. Seed bank Cannings graphs: How dormancy smoothes random genetic drift.
- Author
-
González Casanova, Adrián, Peñaloza, Lizbeth, and Siri-Jégousse, Arno
- Subjects
- *
PLANT gene banks , *DIRECTED graphs , *LIMIT theorems , *POPULATION genetics , *GENEALOGY - Abstract
In this article, we introduce a random (directed) graph model for the simultaneous forwards and backwards description of a rather broad class of Cannings models with a seed bank mechanism. This provides a simple tool to establish a sampling duality in the finite population size, and obtain a path-wise embedding of the forward frequency process and the backward ancestral process. Further, it allows the derivation of limit theorems that generalize celebrated results by Möhle to models with seed banks, and where it can be seen how the effect of seed banks affects the genealogies. The explicit graphical construction is a new tool to understand the subtle interplay of seed banks, reproduction and genetic drift in population genetics. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
46. DOUBLE INERTIAL PARAMETERS FORWARD-BACKWARD SPLITTING METHOD: APPLICATIONS TO COMPRESSED SENSING, IMAGE PROCESSING, AND SCAD PENALTY PROBLEMS.
- Author
-
JOLAOSO, LATEEF OLAKUNLE, YEKINI SHEHU, JEN-CHIH YAO, and RENQI XU
- Subjects
IMAGE processing ,IMAGE segmentation ,ARTIFICIAL neural networks ,IMAGE analysis ,HILBERT space - Abstract
In this paper, a forward-backward splitting algorithm with two inertial parameters (one nonnegative and the other non-positive) extrapolation step is proposed for finding a zero point of the sum of maximal monotone and co-coercive operators in real Hilbert spaces. One of the interesting features of our proposed algorithm is that no online rule on the inertial parameters with the iterates is needed. The weak convergence result of the proposed algorithm is established under some standard assumptions. Numerical results arising from LASSO problems in compressed sensing, image processing, and SCAD penalty problems are provided to illustrate the behavior of our proposed algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
47. Adaptive inertial Yosida approximation iterative algorithms for split variational inclusion and fixed point problems
- Author
-
Mohammad Dilshad, Mohammad Akram, Md. Nasiruzzaman, Doaa Filali, and Ahmed A. Khidir
- Subjects
split variational inclusion ,fixed point problem ,yosida approximation ,algorithms ,weak convergence ,strong convergence ,Mathematics ,QA1-939 - Abstract
In this paper, we present self-adaptive inertial iterative algorithms involving Yosida approximation to investigate a split variational inclusion problem (SVIP) and common solutions of a fixed point problem (FPP) and SVIP in Hilbert spaces. We analyze the weak convergence of the proposed iterative algorithm to explore the approximate solution of the SVIP and strong convergence to estimate the common solution of the SVIP and FPP under some mild suppositions. A numerical example is demonstrated to validate the theoretical findings, and comparison of our iterative methods with some known schemes is outlined.
- Published
- 2023
- Full Text
- View/download PDF
48. On split equality fixed-point problems
- Author
-
L.B. Mohammed, A. Kılıçman, and A.U Saje
- Subjects
Fixed-point problem ,Non-linear mappings ,Iterative algorithm ,Weak convergence ,Engineering (General). Civil engineering (General) ,TA1-2040 - Abstract
In this present work, we study new algorithms to solve the split equality fixed-point problems for total quasi-asymptotically nonexpansive mappings in Hilbert spaces. In addition, we have established the convergence criteria for the proposed algorithms, at the end, we provided numerical results that justified our theoretical results. The results presented in this paper, provided a unified framework for studying this kind of problem involving different classes of mappings.
- Published
- 2023
- Full Text
- View/download PDF
49. A counterexample to the new iterative scheme of Rezapour et al.: Some discussions and corrections
- Author
-
Satit Saejung
- Subjects
common fixed point ,generalized α-nonexpansive mapping ,weak convergence ,strong convergence ,uniformly convex banach space ,strictly convex banach space ,Mathematics ,QA1-939 - Abstract
In this paper, we show a counterexample to the new iterative scheme introduced by Rezapour et al. in "A new modified iterative scheme for finding common fixed points in Banach spaces: application in variational inequality problems" [2]. We propose a modified iteration to conclude the convergence result. Moreover, some of our results are established under a weaker assumption.
- Published
- 2023
- Full Text
- View/download PDF
50. Approximation of fixed point of generalized non-expansive mapping via new faster iterative scheme in metric domain
- Author
-
Noor Muhammad, Ali Asghar, Samina Irum, Ali Akgül, E. M. Khalil, and Mustafa Inc
- Subjects
suzuki generalized non expansive mapping ,uniformly convex metric space ,iteration process ,weak convergence ,strong convergence ,condition (c) ,Mathematics ,QA1-939 - Abstract
In this paper, we establish a new iterative process for approximation of fixed points for contraction mappings in closed, convex metric space. We conclude that our iterative method is more accurate and has very fast results from previous remarkable iteration methods like Picard-S, Thakur new, Vatan Two-step and K-iterative process for contraction. Stability of our iteration method and data dependent results for contraction mappings are exact, correspondingly on testing our iterative method is advanced. Finally, we prove enquiring results for some weak and strong convergence theorems of a sequence which is generated from a new iterative method, Suzuki generalized non-expansive mappings with condition (C) in uniform convexity of metric space. Our results are addition, enlargement over and above generalization for some well-known conclusions with literature for theory of fixed point.
- Published
- 2023
- Full Text
- View/download PDF
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