Ishikawa iteration process for asymptotic pointwise nonexpansive mappings in metric spaces

Buthinah A Bin Dehaish

doi:10.1186/1687-1812-2013-98

Abstract

Let ( M , d ) Open image in new window be a complete 2-uniformly convex metric space, C be a nonempty, bounded, closed and convex subset of M, and T be an asymptotic pointwise nonexpansive self mapping on C. In this paper, we define the modified Ishikawa iteration process in M, i.e.,

Highlights

1 Introduction The class of asymptotic nonexpansive mapping have been extensively studied in fixed point theory since the publication of the fundamental paper [ ]
Kozlowski [ ] proved convergence to a fixed point of some iterative algorithms applied to asymptotic pointwise mappings in Banach spaces
In a recent paper [ ], the authors investigate the existence of a fixed point of asymptotic pointwise nonexpansive mappings and study the convergence of the modified Mann iteration in hyperbolic metric spaces

Summary

Introduction

The class of asymptotic nonexpansive mapping have been extensively studied in fixed point theory since the publication of the fundamental paper [ ]. Kirk and Xu [ ] studied the asymptotic nonexpansive mapping in uniformly convex Banach spaces. Espinola et al [ ] examined the convergence of iterates for asymptotic pointwise contractions in uniformly convex metric spaces.

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Conclusion