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We prove weak convergence of order one for a class of exponential based integrators for SDEs with non-globally Lipschitz drift. Our analysis covers tamed versions of Geometric Brownian Motion (GBM) based methods as well as the standard exponential schemes. The numerical performance of both the GBM and exponential tamed methods through four different multi-level Monte Carlo techniques are compared. We observe that for linear noise the standard exponential tamed method requires severe restrictions on the step size unlike the GBM tamed method. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method for solving variational inclusion problems in Hilbert spaces. This algorithm uses two inertial terms to speed up the convergence. In order to avoid computing the Lipschitz stepsize, we use an updated stepsize which is not necessary to know the Lipschitz constant of the operator. The weak convergence is established under some mild conditions. We present numerical performance of the proposed algorithm and compare our algorithm with other algorithms in literature. Finally, we deduce our algorithm for solving the convex minimization problem and give an application to the data classification problem of heart failure dataset. [ABSTRACT FROM AUTHOR]

We introduce a novel class of asymptotically α-hemicontractive mappings and demonstrate its relationship with the existing related families of mappings. We establish certain interesting properties of the fixed point set of the new class of mappings. Furthermore, we propose and investigate a new iterative algorithm for solving split common fixed point problem for the new class of mappings. In particular, weak and strong convergence theorems for solving split common fixed point problem for our new class of mappings in Hilbert spaces are proved. Moreover, using our method, we require no prior knowledge of norm of the transfer operator. The results presented in the paper extend and improve the results of Censor and Segal [Censor, Y.; Segal, A. The split common fixed point problem for directed operators. J. Convex Anal. 16 (2009), no. 2, 587-600.], Moudafi [Moudafi, A. The split common fixed-point problem for demicontractive mappings. Inverse Problems 26 (2010), no. 5:055007.; Moudafi, A. A note on the split common fixed-point problem for quasi-nonexpansive operators. Nonlinear Anal. 74 (2011), no. 12, 4083-4087.], Chima and Osilike [Chima, E. E.; Osilike, M. O. Split common fixed point problem for class of asymptotically hemicontractive mappings. J. Nigerian Math. Soc. 38 (2019), no. 3, 363-390.], Fan et al [Fan, Q.; Peng, J.; He, H. Weak and strong convergence theorems for the split common fixed point problem with demicontractive operators. Optimization 70 (2021), no. 5-6, 1409-1423.] and host of other related results in literature. [ABSTRACT FROM AUTHOR]

This work is motivated by a gap in the functional data analysis literature, particularly in the context of neuroimaging, regarding the ability of functional models to robustly accommodate intra‐observation dependence. In response, we propose an M‐estimator based on generalized empirical likelihood for the varying‐coefficient model with a functional response. We develop statistical inference procedures, simultaneous confidence regions, and a global general linear hypothesis test for the model's functional coefficient. Our theoretical results establish the weak convergence of the log‐likelihood ratio process, a nonparametric version of Wilks' theorem for the log‐likelihood ratio, and asymptotic properties of the proposed estimator. Through a simulation study, we show that the proposed confidence sets have close‐to‐nominal coverage probabilities. In a real‐world application to a neuroimaging dataset, we show that mini‐mental state examination score and apolipoprotein E genotype have significant associations with fractional anisotropy, while associations with gender and age are only present at high quantile levels. [ABSTRACT FROM AUTHOR]

This manuscript proposes a generalization of weak convergence and study of fixed point in a real Hilbert space for quasi-nonexpanding maps. In this work, we introduce a class of fixed points theorems for nonexpansive mapping and generalized form of nonexpansive mapping under the Hilbert space. In addition, we obtained under quasi nonexpansive mapping weak convergence with respect to Hilbert space by Mann’s Type. [ABSTRACT FROM AUTHOR]

The transition density of the diffusion process plays an important role in calculating the dynamic characteristics of the underlying variables as well as the model estimation. In this article, we combine the idea of conditional probability density function with non parametric kernel regression, and introduce the kernel estimation of joint density function and marginal density function, then construct the non parametric kernel estimator of the transition density of second-order diffusion process based on discrete observational samples. In order to obtain the asymptotic properties of the new kernel estimator, we analyze the asymptotic expectation and asymptotic variance of the proposed estimator under some mild conditions. Finally, the consistency and asymptotic normality of the new proposed non parametric estimator of the transition density function are proved. [ABSTRACT FROM AUTHOR]

In this paper, we introduce generalized difference weak sequence space classes by utilizing the difference operator Δ ı ȷ \Delta^{\jmath}_{\imath} and the de la Vallée–Poussin mean, denoted as [ ( V , λ ) w , Δ ı ȷ ] m [(\mathscr{V},\lambda)_{w},\Delta^{\jmath}_{\imath}]_{m} for m = 0 m=0 , 1, and ∞. Further, we explore some algebraic and topological properties of these spaces, including their nature as linear, normed, Banach, and BK spaces. Additionally, we examine properties such as solidity, symmetry, and monotonicity. Finally, we define and establish some inclusion relations among generalized difference weak statistical convergence, generalized difference weak 휆-statistical convergence, and generalized difference weak [ V , λ ] [\mathscr{V},\lambda] -convergence. [ABSTRACT FROM AUTHOR]

In this article, we introduced the idea of lacunary weak convergence of sequences defined by the class of Orlicz function. Various topological and algebraic properties, such as solidity, symmetry, and monotonicity, have been studied. To validate the failure instances, we gave appropriate examples and detailed discussions. Additionally, we have established some inclusion relationships between these spaces. [ABSTRACT FROM AUTHOR]

We consider a nonlinear, hyperbolic population balance equation that incorporates both aggregation and collisional breakage events simultaneously. Our approach revolves around the development of a novel time-explicit finite volume scheme. Under a suitable time-step stability condition, we prove the convergence of the approximate solution for any non-uniform mesh. A first-order convergence is obtained by a thorough error analysis of the proposed scheme for a suitable choice of kernels. Finally, we compute some numerical test examples to explore the behavior of the solution in steady-state conditions as well as the occurrence of gelation phenomena. [ABSTRACT FROM AUTHOR]

Let (K,d) be a connected compact metric space and p\in (1, \infty). Under the assumption of Kigami [ Conductive homogeneity of compact metric spaces and construction of p-energy , Memoirs of the European Mathematical Society, vol. 5, Europea Mathematical Society (EMS), Berline, 2023, Assumption 2.15] and the conductive p-homogeneity, we show that \mathcal {W}^p(K)\subset C(K) holds if and only if p>\operatorname {dim}_{AR}(K,d), where \mathcal {W}^p(K) is Kigami's (1,p)-Sobolev space and \operatorname {dim}_{AR}(K,d) is the Ahlfors regular dimension. [ABSTRACT FROM AUTHOR]

AbstractIn this article, we study the parameter estimation problem of the continuous-time continuous-state stochastic SIR model in the context of discrete-time observations. Specifically, we propose estimators of the efficient contact rate and recovery rate based on weighted conditional least squares estimators (WCLSEs) and establish the relevant asymptotic distribution of the corresponding estimators under appropriate moment conditions. [ABSTRACT FROM AUTHOR]

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]

We propose a finite element discretization for the steady, generalized Navier-Stokes equations for fluids with shear-dependent viscosity, completed with inhomogeneous Dirichlet boundary conditions and an inhomogeneous divergence constraint. We establish (weak) convergence of discrete solutions as well as a priori error estimates for the velocity vector field and the scalar kinematic pressure. Numerical experiments complement the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we introduce three new inertial-like Bregman projection methods with a nonmonotone adaptive step-size for solving quasi-monotone variational inequalities in real Hilbert spaces. Under some suitable conditions, the weak convergence of these methods is proved without the prior knowledge of the Lipschitz constant of the operator and the strong convergence of some proposed methods under a strong quasi-monotonicity assumption of the mapping is also provided. Finally, several numerical experiments and applications in image restoration problems are provided to illustrate the performance of the proposed methods. [ABSTRACT FROM AUTHOR]

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]

The metric flow is introduced and extensively studied by Bamler [Compactness theory of the space of super Ricci flows, preprint (2020), arXiv:2008.09298; Structure theory of non-collapsed limits of Ricci flows, preprint (2020), arXiv:2009.03243], especially as an 픽-limit of a sequence of smooth Ricci flows with uniformly bounded Nash entropy, in which case each regular point on the limit is a point of smooth convergence. In this note, we shall consider the 픽-convergence of a sequence of 픽-limit flows, and, like Bamler, show that each regular point on the limit is also a point of smooth convergence. The main result will be applied in another work of the authors [P.-Y. Chan, Z. Ma and Y. Zhang, Dimension reduction for positively curved steady solitons, preprint (2023), arXiv:2310.14020]. [ABSTRACT FROM AUTHOR]

In this paper, we consider universality in short intervals for the zeta-function attached to a normalized Hecke-eigen cusp form with respect to the modular group. For this, we apply a conjecture for the mean square in short interval on the critical strip for that zeta-function. The proof of the obtained universality theorem is based on a probabilistic limit theorem in the space of analytic functions. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new inertial iterative algorithm involving the linesearch rule for the split variational inclusion in real Hilbert spaces. We use two inertial terms to accelerate the convergence speed of the proposed algorithm. Under suitable conditions, we prove its weak convergence theorem. Finally, in applications, we apply our algorithm to image deblurring and data classification problem in predicting diabetes mellitus. [ABSTRACT FROM AUTHOR]

In this work, we propose inclusion problems based on a novel class of forward-backwardforward algorithms. Our approach incorporates multi-inertial extrapolations and utilizes a self-adaptive technique to eliminate the need for explicitly selecting Lipschitz assumptions to enhance the speed convergence of the algorithm. We establish a weak convergence theorem under suitable assumptions. Furthermore, we conduct numerical tests on image deblurring as a practical application. The experimental results demonstrate that our algorithm surpasses some existing methods in the literature, which shows its superior performance and effectiveness. [ABSTRACT FROM AUTHOR]

This paper presents a two inertial technique with a projection Mann forward-backward splitting algorithm for solving variational inclusion problems that exhibit weak convergence under suitable conditions in Hilbert spaces. Furthermore, we provide a numerical example in infinitely dimensional spaces to support the main result. Finally, we provide an application for data classification using an extreme learning machine. According to data provided by theWorld Health Organization (WHO), stroke is recognized as the predominant contributor to mortality and disability on a global scale. To appraise the efficacy of our algorithm, we procured a dependable dataset for stroke prediction from the Kaggle website. The best algorithm that performed this task is ours compared to other machine learning methods. [ABSTRACT FROM AUTHOR]

In this work, we propose a novel class of forward‐backward‐forward algorithms for solving monotone inclusion problems. Our approach incorporates a self‐adaptive technique to eliminate the need for explicitly selecting Lipschitz assumptions and utilizes two‐step inertial extrapolations to enhance the convergence rate of the algorithm. We establish a weak convergence theorem under mild assumptions. Furthermore, we conduct numerical tests on image deblurring and data classification as practical applications. The experimental results demonstrate that our algorithm surpasses some existing methods in the literature which shows its superior performance and effectiveness. [ABSTRACT FROM AUTHOR]

We consider optimal control problems for a system governed by a stochastic differential equation driven by a d-dimensional Brownian motion where both the drift and the diffusion coefficient are controlled. It is well known that without additional convexity conditions the strict control problem does not admit an optimal control. To overcome this difficulty, we consider the relaxed model, in which admissible controls are measure-valued processes and the relaxed state process is governed by a stochastic differential equation driven by a continuous orthogonal martingale measure. This relaxed model admits an optimal control that can be approximated by a sequence of strict controls by the so-called chattering lemma. We establish optimality necessary conditions, in terms of two adjoint processes, extending Peng's maximum principle to relaxed control problems. We show that relaxing the drift and diffusion martingale parts directly as in deterministic control does not lead to a true relaxed model as the obtained controlled dynamics is not continuous in the control variable. [ABSTRACT FROM AUTHOR]

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]

Our study in this paper is focused on the split equality fixed-point problem with firmly quasi-non-expansive operators in infinite-dimensional Hilbert spaces. A self-adaptive simultaneous scheme is introduced, and its weak convergence is established under mild and standard assumptions. The new proposed scheme generalizes and extends some related works in the literature, and its simple structure makes it easy for implementation and numerical testing. Primary experiments presented in this paper, in finite- and infinite-dimensional spaces, emphasize their practical advantages over existing results. [ABSTRACT FROM AUTHOR]

In this work, we consider the stochastic Cahn-Hilliard/Allen-Cahn equation with fractional noise, which is fractional in time and white in space. We obtain the existence, uniqueness, and Hölder regularity of the solution. Also, using a weak convergence approach, we prove that the law of solution associated with the above equation with a small perturbation satisfies the large deviation principle in the Hölder norm. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the difference between the deterministic and stochastic models of nonlocal diffusion. We use a nonlocal reaction-diffusion equation and a multi-dimensional jump Markov process to analyze these mathematical models. First, we demonstrate that the difference converges to 0 in probability with a supremum norm for a sizeable network. Next, we consider the rescaled difference and show that it converges to a stochastic process in distribution on the Skorokhod space. [ABSTRACT FROM AUTHOR]

The projected reflected gradient method has been shown to be a simple and elegant method for solving variational inequalities. The method involves one projection onto the feasible set and one evaluation of the cost operator per iteration and has been shown numerically to be more efficient than most available methods for solving variational inequalities. Convergence results for methods with similar elegant structures of projected reflected gradient method are still rare. In this paper, we present weak and linear convergence of a projected reflected gradient method with an inertial extrapolation step and give some applications arising from optimal control problems. We first obtain weak convergence result for the projected reflected gradient method with an inertial extrapolation step for solving variational inequalities under standard assumptions with self-adaptive step sizes. We further obtain a linear convergence rate when the cost operator is strongly monotone and Lipschitz continuous. Finally, we give some numerical applications arising from optimal control. Preliminary results show that our method is effective and efficient when compared to other related state-of-the-art methods in the literature and show the advantage gained by incorporating inertial terms into the projected reflected gradient methods. [ABSTRACT FROM AUTHOR]

We consider the Ginzburg–Landau equation in the perforated domain, with rapidly oscillating coefficients. We derive the homogenized Ginzburg–Landau equation with a 'strange term' (potential) and prove that the trajectory attractors of the given equation tend in a weak sense to the trajectory attractors of the homogenized one. Assuming additional conditions to be satisfied for the coefficients, we provide also a convergence of the global attractor. [ABSTRACT FROM AUTHOR]

We establish a large deviation principle (LDP) for a class of stochastic porous media equations driven by Lévy-type noise on a σ-finite measure space (E,B(E),μ), with the Laplacian replaced by a negative definite self-adjoint operator. One of the main contributions of this paper is that we do not assume the compactness of embeddings in the corresponding Gelfand triple, and to compensate for this generalization, a new procedure is provided. This is the first paper to deal with LDPs for stochastic evolution equations with Lévy noise without compactness conditions. The coefficient Ψ is assumed to satisfy nondecreasing Lipschitz nonlinearity, so an important physical problem covered by this case is the Stefan problem. Numerous examples of negative definite self-adjoint operators are applicable to our results, for example, for open E⊂Rd, L= Laplacian or fractional Laplacians, i.e., L=-(-Δ)α, α∈(0,1], generalized Schrödinger operators, i.e., L=Δ+2∇ρ/ρ⋅∇, Laplacians on fractals is also included. [ABSTRACT FROM AUTHOR]

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]

A modular string averaging procedure (MSA, for short) for a finite number of operators was first introduced by Reich and Zalas in 2016. The MSA concept provides a flexible algorithmic framework for solving various feasibility problems such as common fixed point and convex feasibility problems. In 2001 Bauschke and Combettes introduced the notion of coherence and applied it to proving weak and strong convergence of many iterative methods. In 2019 Barshad, Reich and Zalas proposed a stronger variant of coherence which provides a more convenient sufficient convergence condition for such methods. In this paper we combine the ideas of both modular string averaging and coherence. Focusing on extending the above MSA procedure to an infinite sequence of operators with admissible controls, we establish strong coherence of its output operators. Various applications of these concepts are presented with respect to weak and strong convergence. They also provide important generalizations of known results, where the weak convergence of sequences of operators generated by the MSA procedure with intermittent controls was considered. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an inertial accelerated algorithm for solving the split equality common fixed-point problem of directed operators in real Hilbert space. Our algorithm includes the simultaneous iterative algorithm as special case which has been proposed by Moudafi and Al-Shemas for solving the split equality common fixed-point problem. We establish a weak convergence theorem for the proposed iterative algorithm, which combines the primal-dual method and the inertial technique. In our algorithm, the step sizes are chosen self-adaptively so that the implementation of the algorithm does not need any prior information about bounded linear operator norms. The efficiency of the proposed algorithm is illustrated by some numerical experiments. [ABSTRACT FROM AUTHOR]

A new numerical approximation method for a class of Gaussian random fields on compact connected oriented Riemannian manifolds is introduced. This class of random fields is characterized by the Laplace–Beltrami operator on the manifold. A Galerkin approximation is combined with a polynomial approximation using Chebyshev series. This so-called Galerkin–Chebyshev approximation scheme yields efficient and generic sampling algorithms for Gaussian random fields on manifolds. Strong and weak orders of convergence for the Galerkin approximation and strong convergence orders for the Galerkin–Chebyshev approximation are shown and confirmed through numerical experiments. [ABSTRACT FROM AUTHOR]

This paper presents a fully adaptive iterative method without linesearch procedure to solve variational inequalities in the setting of quasi-monotone which is locally Lipschitz. Our method involves one functional evaluation alongside one projection per iteration and our stepsizes are not restricted to be nonincreasing as opposed to relevant methods without linesearch procedure but with nonincreasing stepsizes. We give weak and strong convergence analysis of the sequences generated by our proposed method under some mild conditions. We also give R -linear rate convergence under an error bound condition and give some numerical implementations of our method. Numerical results show that our proposed method is competitive with other related methods in the literature. [ABSTRACT FROM AUTHOR]

We first establish weak convergence results regarding an inertial Krasnosel'skiĭ-Mann iterative method for approximating common fixed points of countable families of nonexpansive mappings in real Hilbert spaces with no extra assumptions on the considered countable families of nonexpansive mappings. The method of proof and the imposed conditions on the iterative parameters are different from those already available in the literature. We then present some applications to the Douglas–Rachford splitting method and image restoration problems, and compare the performance of our method with that of other popular inertial Krasnosel'skiĭ-Mann methods which can be found in the literature. [ABSTRACT FROM AUTHOR]

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]

The multistage stochastic variational inequality is reformulated into a variational inequality with separable structure through introducing a new variable. The prediction–correction ADMM which was originally proposed in He et al. (J Comput Math 24:693–710, 2006) for solving deterministic variational inequalities in finite-dimensional spaces is adapted to solve the multistage stochastic variational inequality. Weak convergence of the sequence generated by that algorithm is proved under the conditions of monotonicity and Lipschitz continuity. When the sample space is a finite set, the corresponding multistage stochastic variational inequality is actually defined on a finite-dimensional Hilbert space and the strong convergence of the algorithm naturally holds true. Some numerical examples are given to show the efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

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]

This paper derives a free analogue of the Euler-Maruyama method (fEMM) to numerically approximate solutions of free stochastic differential equations (fSDEs). Simply speaking, fSDEs are SDEs in the context of noncommutative random variables (e.g., large random matrices). By applying the theory of multiple operator integrals, we derive a free Itô formula from Taylor expansion of operator-valued functions. Iterating the free Itô formula allows us to motivate and define fEMM. Then we consider weak and strong convergence in the fSDE setting and prove strong convergence order of 1/2 and weak convergence order of 1. Numerical examples support the theoretical results and show solutions for equations where no analytical solution is known. [ABSTRACT FROM AUTHOR]

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]

In this paper, we introduce two modified Tseng's extragradient algorithms with a new generalized adaptive stepsize for solving monotone variational inequalities (VI) in reflexive Banach spaces. The advantage of our methods is that stepsizes do not require prior knowledge of the Lipschitz constant of the cost mapping. Based on Bregman projection-type methods, we prove weak and strong convergence of the proposed algorithms to a solution of VI. Some numerical experiments to show the efficiency of our methods including a comparison with related methods are provided. [ABSTRACT FROM AUTHOR]

We propose an extension of the Cox-Ross-Rubinstein (CRR) model based on q-binomial (or Kemp) random walks, with application to default with logistic failure rates. This model allows us to consider time-dependent switching probabilities varying according to a trend parameter on a non-self-similar binomial tree. In particular, it includes tilt and stretch parameters that control increment sizes. Option pricing formulas are written using q-binomial coefficients, and we study the convergence of this model to a Black-Scholes type formula in continuous time. A convergence rate of order O(N-1/2) is obtained. [ABSTRACT FROM AUTHOR]

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]

In the paper we consider a problem for complex Ginzburg–Landau equations in a medium with locally periodic small obstacles. It is assumed that the obstacle surface can have different conductivity coefficients. We prove that the trajectory attractors of this system converge in a certain weak topology to the trajectory attractors of the homogenized Ginzburg–Landau equations with an additional potential (in the critical case), without an additional potential (in the subcritical case) in the medium without obstacles, or disappear (in the supercritical case). [ABSTRACT FROM AUTHOR]

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]

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]

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]