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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.

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]

Hadamard spaces have traditionally played important roles in geometry and geometric group theory. More recently, they have additionally turned out to be a suitable framework for convex analysis, optimization and non-linear probability theory. The attractiveness of these emerging subject fields stems, inter alia, from the fact that some of the new results have already found their applications both in mathematics and outside. Most remarkably, a gradient flow theorem in Hadamard spaces was used to attack a conjecture of Donaldson in Kähler geometry. Other areas of applications include metric geometry and minimization of submodular functions on modular lattices. There have been also applications into computational phylogenetics and image processing. We survey recent developments in Hadamard space analysis and optimization with the intention to advertise various open problems in the area. We also point out several fallacies in the existing proofs. [ABSTRACT FROM AUTHOR]

To address the split best proximity point and monotone variational inclusion problems in real Hilbert spaces, we present and investigate projection and viscosity approximation methods. Under a few reasonable assumptions, we prove some weak and strong convergence theorems for the aforementioned methods. The efficiency of the proposed method is demonstrated by some numerical examples. Some well-known recent results in this area have been improved, generalized, and extended as an outcome of this paper. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the convex minimization problem in real Hilbert spaces. We introduce a new relaxed forward-backward-forward method by using the inertial technique and the adaptive stepsize. We then provide its convergence theorem under suitable assumptions. Finally, we analyse the proposed method to image inpainting and give comparisons of our method with other methods in the literature. [ABSTRACT FROM AUTHOR]

This work focuses on stochastic functional differential equations (SFDEs) with wide-band noise perturbation, which is a class of actual physical process and has wide application in the modeling of communication and signal system. Using functional derivatives together with martingale methods and weak convergence techniques, this paper examines the asymptotic properties of the underlying systems as the small parameter tends to zero. Based on the techniques, this paper also establishes the average principle for a class of SFDEs with two-time scales. As a special case, this paper also considers a class of integro-differential equations with wide-band noise perturbation and examines its approximate properties. As an example, a scalar stochastic Lotka–Volterra integro-differential system with wide-band noise perturbation is investigated. [ABSTRACT FROM AUTHOR]

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]

We come up with a new type of forward–backward–forward algorithms for monotone inclusion problems based on a self-adaptive technique to avoid the selection of Lipschitz assumption and also double inertial extrapolations to increase the convergence performance of our presented algorithm. We also prove its weak convergence theorem under mild hypothesis. Additionally, we provide numerical test in image deblurring and signal recovery as applications. The results show that our algorithm outperforms some known algorithms in the literature. [ABSTRACT FROM AUTHOR]

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]

In this paper, we study the weak convergence and convergence rate in the weak law of large numbers for weighted sums of a class of random variables satisfying the Rosenthal type inequality. The necessary and sufficient conditions for the convergence rates in the weak law of large numbers under some mild conditions are provided. Moreover, the main results that we established are applied to simple linear errors-in-variables regression models and nonparametric regression models based on a class of random errors. Finally, we present some numerical simulations to assess the finite sample performance of the theoretical results. [ABSTRACT FROM AUTHOR]

The two-dimensional system of Navier–Stokes equations in a medium with anisotropic variable viscosity and periodic small obstacles is considered. It is proved that the trajectory attractors of the system tend in a certain weak topology to the trajectory attractors of the homogenized system of Navier–Stokes equations with an additional potential in a medium without obstacles. [ABSTRACT FROM AUTHOR]

Let N t (n) denote the number of blocks in a Ξ -coalescent restricted to a sample of size n ∈ N after time t ≥ 0. Under the assumption of a certain curvature condition on a function well-known from the literature, we prove the existence of sequences (v (n , t)) n ∈ N for which (log N t (n) − log v (n , t)) t ≥ 0 converges to an Ornstein–Uhlenbeck type process as n → ∞. The curvature condition is intrinsically related to the behavior of Ξ near the origin. The method of proof is to show the uniform convergence of the associated generators. Via Siegmund duality an analogous result for the fixation line is proven. Several examples are studied. [ABSTRACT FROM AUTHOR]

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]

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.

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.

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]

Each sequence f1, f2, ... of random variables satisfying limM→∞ (M supk∈N P(|fk| > M)) = 0 contains a subsequence fk1, fk2, ??? which, along with all its subsequences, satisfies the weak law of large numbers limN→∞ ((1/N) ∑n=1N fkn -- DN) = 0 in probability. Here, DN is a "corrector" random variable with values in [--N, N] for each N ∈ N; these correctors are all equal to zero if, in addition, lim infn→∞ E (fn² 1{|fn|≤M})) = 0 for every M ∈ (0, ∞). [ABSTRACT FROM AUTHOR]

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]

In the present paper, we propose a local discontinuous Galerkin approximation for fully nonhomogeneous systems of p-Navier--Stokes type. On the basis of the primal formulation, we prove well-posedness, stability (a priori estimates), and weak convergence of the method. To this end, we propose a new discontinuous Galerkin discretization of the convective term and develop an abstract nonconforming theory of pseudomonotonicity, which is applied to our problem. We also use our approach to treat the p-Stokes problem. [ABSTRACT FROM AUTHOR]

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]

In this article, we enquire for some weak and strong convergence results for a class of mappings satisfying Condition (E) via Picard Normal S-iterative algorithm (PNSA) in the setting of uniformly convex Banach space (UCBS). Eventually, we furnish an example to substantial our attained findings and numerically compare PNSA with that of some other well-known iterative algorithms. Additionally, we discuss the existence of the solution of a nonlinear functional integral equation as an application of our result. [ABSTRACT FROM AUTHOR]

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.

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.

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.

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.

In this paper the Ginzburg-Landau equation is considered in locally periodic porous medium, with rapidly oscillating terms in the equation and boundary conditions. It is proved that the trajectory attractors of this equation converge in a weak sense to the trajectory attractors of the limit Ginzburg-Landau equation with an additional potential term. For this aim we use an approach from the papers and monographs of V.V. Chepyzhov and M.I. Vishik concerning trajectory attractors of evolution equations. Also we apply homogenization methods appeared at the end of the XX-th century. First, we apply the asymptotic methods for formal construction of asymptotics, then, we verify the leading terms of asymptotic series by means of the methods of functional analysis and integral estimates. Defining the appropriate axillary functional spaces with weak topology, we derive the limit (homogenized) equation and prove the existence of trajectory attractors for this equation. Then we formulate the main theorem and prove it with the help of axillary lemmas.

This paper is devoted to the approximation of a certain class of analytic functions by shifts Z (s + i τ) , τ ∈ R , of the modified Mellin transform Z (s) of the square of the Riemann zeta-function ζ (1 / 2 + i t) . More precisely, we prove the existence of a closed non-empty set F such that there are infinitely many shifts Z (s + i τ) , which approximate a given analytic function from F with a given accuracy. In the proof, the weak convergence of measures in the space of analytic functions is applied. Then, the set F coincides with the support of a limit measure. [ABSTRACT FROM AUTHOR]

Numerical solutions of stochastic problems involve approximations of the random functions in their definitions by deterministic functions of time and/or space and finite numbers of random variables, referred to as finite dimensional (FD) random functions. Since the solutions of these problems are complex functionals of random functions, the resulting numerical solutions are informative only if target random functions and their FD representations have similar samples. We establish conditions under which extremes and other functionals of real-valued continuous processes X(t) can be estimated from samples of FD processes X d (t) . Four types of FD processes are developed for stationary and nonstationary processes X(t). Numerical examples are presented to illustrate the construction of these FD processes and assess their capabilities to characterize extremes of X(t). [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The life distribution of a device subject to shocks governed by a homogeneous Poisson process is shown to have a bathtub failure rate average (BFRA) when the probabilities $\bar{P}_k$ of surviving k shocks possess the corresponding discrete property. We prove closure under the formation of weak limits for BFRA distributions and explore related moment convergence issues within the BFRA family. Similar results for increasing and decreasing failure rate average distributions are obtained either independently or as consequences of our results. We also establish some results outlining the positions of various non-monotonic ageing classes such as bathtub failure rate, increasing initially then decreasing mean residual life, new worse then better than used in expectation, and increasing initially then decreasing mean time to failure in the hierarchy. Finally, an open problem is posed and a partial solution provided. [ABSTRACT FROM AUTHOR]

The problem of optimally scaling the proposal distribution in a Markov chain Monte Carlo algorithm is critical to the quality of the generated samples. Much work has gone into obtaining such results for various Metropolis–Hastings (MH) algorithms. Recently, acceptance probabilities other than MH are being employed in problems with intractable target distributions. There are few resources available on tuning the Gaussian proposal distributions for this situation. We obtain optimal scaling results for a general class of acceptance functions, which includes Barker's and lazy MH. In particular, optimal values for Barker's algorithm are derived and found to be significantly different from that obtained for the MH algorithm. Our theoretical conclusions are supported by numerical simulations indicating that when the optimal proposal variance is unknown, tuning to the optimal acceptance probability remains an effective strategy. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two algorithms for finding a common solution of the monotone inclusion problem and the fixed point problem for a relatively nonexpansive mapping in reflexive Banach spaces. The weak convergence results for both algorithms are established without the prior knowledge of the Lipschitz constant of the mapping. An application to the variational inequality problem is considered. Finally, some numerical experiments of the proposed algorithms including comparisons with other algorithms are provided. [ABSTRACT FROM AUTHOR]

In this paper, by combining the hyperplane projection technique and gradient projection method with Polyak’s stepsizes, we propose a novel projection algorithm to solve the split feasibility problem in Hilbert spaces. Unlike the existing projection methods, our method is designed such that the next iterate is closer to the solution set than the previous one. The weak and strong convergence of new algorithms under standard assumptions are established. We examine the performance of our method on the sparse signal recovery problem. The reported numerical results demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Projection methods have been one of the popular methods for solving variational inequality problems in the literature. Several projection methods have been studied for variational inequality problems and most of these methods require at least two evaluations of the cost operator and (or) two projections per iteration. One of the major interests of researchers in variational inequalities is to study projection methods with less computational complexity in terms of reduced number of evaluations of the cost operator and reduced number of projections onto feasible set per iteration especially when the cost operator is non-monotone. In this paper, we propose a simple projection method which requires only one evaluation of the cost operator and one projection onto the feasible set per iteration. We obtain weak convergence results when the cost operator is quasimonotone and Lipschitz continuous with self-adaptive line search strategy. We also give weak convergence analysis when the cost operator is non-monotone and Lipschitz continuous. Some numerical implementations using standard tests are given to illustrate our method and compare with other recently related methods. [ABSTRACT FROM AUTHOR]

In the paper, it is obtained that there are infinite discrete shifts Ξ (s + i k h) , h > 0 , k ∈ N 0 of the Mellin transform Ξ (s) of the square of the Riemann zeta-function, approximating a certain class of analytic functions. For the proof, a probabilistic approach based on weak convergence of probability measures in the space of analytic functions is applied. [ABSTRACT FROM AUTHOR]

In this paper, a theorem is obtained on the approximation in short intervals of a collection of analytic functions by shifts (ζ (s + i t k α 1) , ... , ζ (s + i t k α r)) of the Riemann zeta function. Here, { t k : k ∈ N } is the sequence of Gram numbers, and α 1 , ... , α r are different positive numbers not exceeding 1. It is proved that the above set of shifts in the interval [ N , N + M ] , here M = o (N) as N → ∞ , has a positive lower density. For the proof, a joint limit theorem in short intervals for weakly convergent probability measures is applied. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new inertial relaxed CQ algorithm for solving split feasibility problems in Hilbert spaces. The main advantages of the proposed algorithm are that the introduced stepsize is bounded away from zero and relaxation parameter sequences imposed on the stepsize itself are removed. These features help accelerate our method. Also, a weak convergence theorem for our method is established without Lipschitz continuous and firmly-nonexpasive conditions of split feasibility problem related gradient and projection mappings, respectively. As an application, we consider multiple-sets split feasiblity problems. Finally, some preliminary numerical experiments are provided for illustration and comparison. [ABSTRACT FROM AUTHOR]

Recently in Dvurečenskij and Zahiri (J Appl Log IfCoLog J Log Appl 8:2365–2399, 2021b, J Appl Log IfCoLog J Log Appl 8:2401–2433, 2021c), new algebras, called weak pseudo EMV-algebras (wPEMV-algebras in short), were introduced. The authors do not assume the existence of a top element —they generalize MV-algebras, pseudo MV-algebras, and pseudo EMV-algebras. A g-state is defined on a unital wPEMV-algebra M as a mapping from M into the positive half-line of reals such that it preserves a partial addition + , and in a fixed strong unit, it takes the value 1. They form a Bauer simplex, and extremal points are exactly g-states whose kernel is a maximal and normal ideal. We show that extremal g-states generate all g-states, and it can happen that in some unital wPEMV-algebra, even commutative, there is no g-state. We present some conditions for existence of g-states and establish an integral representation of g-states. In addition, we give a topological characterization of the spaces of g-states and extremal g-states, respectively. Moreover, discrete g-states are investigated. [ABSTRACT FROM AUTHOR]

We study the weak convergence of a greedy algorithm of approximation by a given set in a Banach space. It is proved that the greedy algorithm of approximation by a strongly norm-reducing set in a uniformly smooth Banach space with the WN-property weakly converges. In an arbitrary separable Banach space without the WN-property, we construct an example of a strongly norm-reducing set such that the greedy algorithm of approximation by this set does not weakly converge for some initial element. [ABSTRACT FROM AUTHOR]

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. W. Stute [Ann. Probab. 19 (1991) 812–825] 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 : m (t) : = E [ φ (Y 1 , ... , Y m) | (X 1 , ... , X m) = t ] , for t ∈ X m. In this paper we are mainly interested in establishing weak convergence of 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 conditional U-processes when the explicative variable is functional. We treat the weak convergence in both cases when the class of functions is bounded or unbounded satisfying some moment conditions. 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 many further developments in functional data analysis. [ABSTRACT FROM AUTHOR]

Let G : H → H and K : H → H be monotone mappings that are either sequentially weakly continuous or continuous, where H is a real Hilbert space. In this work, we introduce two new iterative methods for approximating solutions of the Hammerstein equation u + G K u = 0 , if they exist. The first iterative method is shown to always converge weakly to an element in the solution set of the Hammerstein equation if this solution set is nonempty. The second iterative method is a modification of the first method to upgrade weak convergence to strong convergence. Convergence results are obtained without requiring the maps to be bounded. Numerical examples are provided to demonstrate the convergence of one of these methods. Comparisons with some existing methods show that the method is cost effective in terms of the number of iterations required to obtain a solution and the computational time. [ABSTRACT FROM AUTHOR]

We study the problem of the existence of a coordinate network of curves on a -smooth bordered surface consisting of geodesic lines covering it up to the set of zero Hausdorff measure and lines orthogonal to them. We additionally assume that the surface is symmetric with respect to some geodesic line. Finding this kind of network is reduced to finding a solution to the nonlinear conjugate Beltrami equation in the unit disk, which degenerates at the points at which the Jacobian of the mapping, carried out by the solution, turns to either zero or infinity. The need for this kind of parametrization is associated with the search for equilibrium forms of liquid droplets in a model that takes into account the presence of an intermediate layer when studying the equilibrium state of a two-phase medium. Using the two-fold method of successive approximations, we establish the presence of a mapping of the unit disk to itself satisfying the Beltrami equation. The constructed mapping is continuous on the closed disk. The real part of the map has the generalized first order derivatives square-integrable on the upper half of the disk and the generalized first order derivatives of the imaginary part are locally square-integrable on it, and the map has the Lusin property. The inverse map, defined almost everywhere on the disk, is almost everywhere injective in it and has the Lusin property. The map found defines an almost global semi-geodesic parametrization of the surface and is a natural generalization of the -quasi-conformal maps introduced by R. Finn and J. Serrin. [ABSTRACT FROM AUTHOR]

In this work, we propose and study a framework of generalized proximal point algorithms associated with a maximally monotone operator. We indicate sufficient conditions on the regularization and relaxation parameters of generalized proximal point algorithms for the equivalence of the boundedness of the sequence of iterations generated by this algorithm and the non-emptiness of the zero set of the maximally monotone operator, and for the weak and strong convergence of the algorithm. Our results cover or improve many results on generalized proximal point algorithms in our references. Improvements of our results are illustrated by comparing our results with related known ones. [ABSTRACT FROM AUTHOR]

The focus of this paper is to obtain weak and linear convergence analysis of the subgradient extragradient method with alternated inertial step for solving equilibrium problems in real Hilbert spaces. The proposed method uses self-adaptive step sizes. Weak convergence is established without Lipschitz constant of the bifunction as an input parameter. Linear convergence is obtained without the modulus of strong pseudomonotonicity and Lipschitz constant as input parameters. We report some priori and posteriori error estimates and some numerical experiments to illustrate the behavior of our proposed method with related methods. [ABSTRACT FROM AUTHOR]

The mann fixed point algorithm play an importmant role in the approximation of fixed points of nonexpansive operators. In this paper, by considering new conditions, we prove the weak convergence of mann fixed point algorithm, for finding a common fixed point of two nonexpansive mappings in real Hilbert spaces. This results extend the privious results given by Kanzow and Shehu. Finally, we give an application of our results, by using the John von Neumann's method.

In this paper, the split feasibility problem is studied in real Banach spaces. Through the W-mapping, a new iterative algorithm with the inertial technique for solving the split feasibility problem is proposed, which the step size is self-adaptive and no prior estimation of operator norm is required. We prove that the proposed algorithm converges weakly to a solution of the split feasibility problem under some mild conditions. Finally, the effectiveness of the proposed algorithm is indicated by numerical experiments. Our results are innovative and can enrich recently announced related results in the literature.