Convergence analysis of generalized viscosity implicit rules for a nonexpansive semigroup with gauge functions

Convergence theorems of implicit iterates with errors for generalized asymptotically quasi-nonexpansive mappings in Banach spaces

In this paper, we prove that an implicit iterative process with er-rors converges strongly to a common xed point for a nite family of generalizedasymptotically quasi-nonexpansive mappings on unbounded sets in a uniformlyconvex Banach space. Our results unify, improve and generalize the correspond-ing results of Ud-din and Khan [4], Sun [21], Wittman [23], Xu and Ori [26] andmany others.

Strong convergence theorems for the generalized viscosity implicit rules of nonexpansive mappings in uniformly smooth Banach spaces

The aim of this paper is to introduce the generalized viscosity implicit rules of one nonexpansive mapping in uniformly smooth Banach spaces. Strong convergence theorems of the rules are proved under certain assumptions imposed on the parameters. As applications, we use our main results to solve fixed point problems of strict pseudocontractions in Hilbert spaces and variational inequality probl...

A General Iterative Method for a Nonexpansive Semigroup in Banach Spaces with Gauge Functions

Strong Convergence Theorem for Semigroup of Asymptotically Nonexpansive Mappings Using Viscosity Approximation

Abstract. Viscosity method also called elliptic regularization, provide an efficient approach to a large number of problems coming from different branches of mathematical and physical sciences. One of the recent trend in the iterative construction of fixed point of nonlinear mappings is to use viscosity approximation method. In this paper we propose implicit and explicit viscosity method (VAM) ...

Convergence Theorem for a Family of Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces

Let E be a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm. Let J {T t : t ≥ 0} be a family of uniformly asymptotically regular generalized asymptotically nonexpansive semigroup of E, with functions u, v : 0,∞ → 0,∞ . Let F : F J ∩t≥0F T t / ∅ and f : K → K be a weakly contractive map. For some positive real numbers λ and δ satisfying δ λ > 1, let G ...