Iterative scheme for a nonexpansive mapping, an η-strictly pseudo-contractive mapping and variational inequality problems in a uniformly convex and 2-uniformly smooth Banach space

Iterative Process for an α- Nonexpansive Mapping and a Mapping Satisfying Condition(C) in a Convex Metric Space

We construct one-step iterative process for an α- nonexpansive mapping and a mapping satisfying condition (C) in the framework of a convex metric space. We study △-convergence and strong convergence of the iterative process to the common fixed point of the mappings. Our results are new and are valid in hyperbolic spaces, CAT(0) spaces, Banach spaces and Hilbert spaces, simultaneously.

Convergence of Implicit and Explicit Schemes for an Asymptotically Nonexpansive Mapping in q-Uniformly Smooth and Strictly Convex Banach Spaces

Implicit Iterative Scheme for a Countable Family of Nonexpansive Mappings in 2-Uniformly Smooth Banach Spaces

and Applied Analysis 3 Our results improve and extend the corresponding conclusions announced by many others. 2. Preliminaries Let S X = {x ∈ X :‖ x ‖= 1}. Then the norm of X is said to be Gâteaux differentiable if

Nonexpansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces

In this paper, most of classical and modern convergence theorems of iterative schemes for nonexpansive mappings are presented and the main results in the paper generalize and improve the corresponding results given by many authors. 2000 Mathematics Subject Classification: Primary 47H17; secondary 47H05, 47H10.

Composite Iterative Algorithms for Variational Inequality and Fixed Point Problems in Real Smooth and Uniformly Convex Banach Spaces

We introduce composite implicit and explicit iterative algorithms for solving a general system of variational inequalities and a common fixed point problem of an infinite family of nonexpansive mappings in a real smooth and uniformly convex Banach space.These composite iterative algorithms are based on Korpelevich’s extragradient method and viscosity approximation method. We first consider and ...