Related papers: Krasnoselskij-type algorithms for variational ineq…
This paper deals with quasi-variational inequality problems (QVIs) in a generic Banach space setting. We provide a theoretical framework for the analysis of such problems which is based on two key properties: the pseudomonotonicity (in the…
Our aim in this paper is to present results of existence of fixed points for continuous operators in Banach spaces using measure of noncompactness under an integral condition. This results are generalization of results given by A. Aghajania…
In this paper, we introduce a new modified Ishikawa iteration for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of relatively nonexpansive mappings in a Banach space. Our results…
In this paper we develop new applications of variational analysis and generalized differentiation to the following optimization problem and its specifications: given n closed subsets of a Banach space, find such a point for which the sum of…
Finding the solutions of nonlinear operator equations has been a subject of research for decades but has recently attracted much attention. This paper studies the convergence of a newly introduced viscosity implicit iterative algorithm to a…
In this article, we develop an algorithm suitable for constrained optimization in $\mathbb{R}^n$. The results are developed through standard tools of n-dimensional real analysis and basic concepts of optimization. Indeed, the well known…
We introduce kernels and resolvents on preordered sets and derive sharp resolvent inequalities that entail Gronwall inequalities for functions of several variables. In this way, we can prove a fixed point result for operators on topological…
We investigate the Stochastic Krasnoselskii-Mann iterations for expected nonexpansive fixed-point problems in a real Hilbert space. We establish convergence guarantees under significantly weaker assumptions on the variance than those…
We prove weak and strong convergence theorems for a double Krasnoselskij type iterative method to approximate coupled solutions of a bivariate nonexpansive operator F : C x C --> C, where C is a nonempty closed and convex subset of a…
This paper is concerned with the differential sensitivity analysis of variational inequalities in Banach spaces whose solution operators satisfy a generalized Lipschitz condition. We prove a sufficient criterion for the directional…
In this paper we present some new results on the existence of solutions of generalized variational inequalities in real reflexive Banach spaces with Fr\'echet differentiable norms. Moreover, we also give some theorems about the structure of…
We obtain results on the existence and approximation of fixed points of enriched contractions in quasi-Banach spaces and thus extend the results obtained in the case of contractions defined on Banach spaces [Berinde, V.; P\u{a}curar, M.…
This paper addresses Tikhonov like regularization methods with convex penalty functionals for solving nonlinear ill-posed operator equations formulated in Banach or, more general, topological spaces. We present an approach for proving…
Averaged operators have played an important role in fixed point theory in Hilbert spaces. They emerged as a necessity to obtain solutions to fixed point problems where the underlying operator is not contractive and thus renders Banach fixed…
This article investigates the convergence properties of s-numbers of certain truncations of bounded linear operators between Banach spaces. We prove a generalized version of a known convergence result for the approximation numbers of…
We adopt an operator-theoretic perspective to analyze a class of nonlinear fixed-point iterations and discrete-time dynamical systems. Specifically, we study the Krasnoselskij iteration - at the heart of countless algorithmic schemes and…
Two-points nonlocal problem for the first order differential evolution equation with an operator coefficient in a Banach space $X$ is considered. An exponentially convergent algorithm is proposed and justified in assumption that the…
In this paper, we prove several fixed point theorems on both of normal partially ordered Banach spaces and regular partially ordered Banach spaces by using the normality, regularity, full regularity, and chain -complete property. Then, by…
Convergence rates results for Tikhonov regularization of nonlinear ill-posed operator equations in abstract function spaces require the handling of both smoothness conditions imposed on the solution and structural conditions expressing the…
We provide new results regarding the localization of the solutions of nonlinear operator systems. We make use of a combination of Krasnosel'ski\u{\i} cone compression-expansion type methodologies and Schauder-type ones. In particular we…