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The aim of this paper is to establish a strong convergence theorem for a strongly nonexpansive sequence in a Banach space. We also deal with some applications of the convergence theorem.

Functional Analysis · Mathematics 2025-09-17 Koji Aoyama , Masashi Toyoda

In this paper, a strong convergence theorem for asymptotically nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem extends and improves the recent strong convergence…

Functional Analysis · Mathematics 2011-12-01 Hossein Dehghan

We present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach's Fixed Point Theorem, ultrametric and certain topological fixed point theorems. It works in a minimal setting, not…

Commutative Algebra · Mathematics 2013-04-02 Katarzyna Kuhlmann , Franz-Viktor Kuhlmann

We prove strong convergence theorems of some iterative algorithms in a real uniformly smooth Banach space. The results presented extend, generalize and improve the corresponding results recently announced by many authors.

Functional Analysis · Mathematics 2015-08-28 Abba Auwalu

Let $\Omega$ be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space $\mathcal{X}$ with dual space $\mathcal{X}^*$. This article presents a hybrid algorithm for finding a common element of the set…

Functional Analysis · Mathematics 2025-09-30 Peter U. Nwokoro , Maria A. Onyido , Markjoe O. Uba , Cyril I. Udeani

In this paper, we introduce a novel two-point gradient method for solving the ill-posed problems in Banach spaces and study its convergence analysis. The method is based on the well known iteratively regularized Landweber iteration method…

Numerical Analysis · Mathematics 2022-05-12 Gaurav Mittal , Ankik Kumar Giri

The aim of this paper is to present an extragradient method for variational inequality associated to a point-to-set vector field in Hadamard manifolds and to study its convergence properties. In order to present our method the concept of…

Optimization and Control · Mathematics 2018-04-26 E. E. A. Batista , G. C. Bento , O. P. Ferreira

We introduce an iterative process for finding common fixed point of finite family of quasi-Bregman nonexpansive mappings which is a unique solution of some equilibrium problem.

Functional Analysis · Mathematics 2017-06-23 G. C. Ugwunnadi , Bashir Ali

In this paper, we prove some theorems related to properties of generalized symmetric hybrid mappings in Banach spaces. Using Banach limits, we prove a fixed point theorem for symmetric generalized hybrid mappings in Banach spaces. Moreover,…

Functional Analysis · Mathematics 2014-11-25 Fridoun Moradlou , Sattar Alizadeh

The $m$-point nonlocal problem for the first order differential equation with an operator coefficient in a Banach space $X$ is considered. An exponentially convergent algorithm is proposed and justified provided that the operator…

Numerical Analysis · Mathematics 2010-01-27 Vitalii Vasylyk , Dmytro Sytnyk

The objective of this paper is to introduce and study a complicated nonlinear system, called coupled variational-hemivariational inequalities, which is described by a highly nonlinear coupled system of inequalities on Banach spaces. We…

Analysis of PDEs · Mathematics 2023-09-12 YR. Bai , S. Migorski , VT. Nguyen , JW. Peng

In this paper, we propose and analyze a two-point gradient method for solving inverse problems in Banach spaces which is based on the Landweber iteration and an extrapolation strategy. The method allows to use non-smooth penalty terms,…

Numerical Analysis · Mathematics 2018-12-31 Min Zhong , Wei Wang , Qinian Jin

In this paper, we study the existence of solutions for generalized vector quasi-equilibrium problems. Firstly, we prove that in the case of Banach spaces, the assumptions of continuity over correspondences can be weakened. The theoretical…

Optimization and Control · Mathematics 2016-05-12 Monica Patriche

A branch of generalizations of the Banach Fixed Point Theorem replaces contractivity by a weaker but still effective property. The aim of the present note is to extend the contraction principle in this spirit for such complete semimetric…

Functional Analysis · Mathematics 2017-06-29 Mihály Bessenyei , Zsolt Páles

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…

Optimization and Control · Mathematics 2017-08-04 Nga Quynh Nguyen

In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing nonzero normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different…

Optimization and Control · Mathematics 2019-02-25 J. Y. Bello Cruz , R. Díaz Millán , Hung M. Phan

In this paper we study the convergence of an iterative algorithm for finding zeros with constraints for not necessarily monotone set-valued operators in a reflexive Banach space. This algorithm, which we call the proximal-projection method…

Exactly Solvable and Integrable Systems · Physics 2007-11-16 Dan Butnariu , Gabor Kassay

The article deals with the generalized Newton--Kantorovich method for solving operator equations with nondifferentiable operators in Banach spaces. The convergence theorem is proved by means of majorant scalar equations.

Numerical Analysis · Mathematics 2012-01-12 A. N. Tanyhina

In this paper, we explain a new Iterative Method-Fixed Point and develop its convergence theory for finding approximate solutions of nonlinear equations in the setting of Banach spaces. First, we discuss the convergence analysis of our…

General Mathematics · Mathematics 2022-05-10 Nikos Mantzakouras , Eteri Biragova

In this paper, we present some common fixed point theorems for a commuting pair of mappings, including a generalized nonexpansive single valued mapping and a generalized nonexpansive multivalued mapping in strictly convex Banach spaces. The…

Functional Analysis · Mathematics 2011-02-09 Ali Abkar , Mohammad Eslamian