A Modified Averaging Composite Implicit Iteration Process for Common Fixed Points of a Finite Family of k-Strictly Asymptotically Pseudocontractive Mappings

Donatus Ikechi Igbokwe ,Oku Ini

doi:10.4236/apm.2011.14036

Abstract

The composite implicit iteration process introduced by Su and Li [J. Math. Anal. Appl. 320 (2006) 882-891] is modified. A strong convergence theorem for approximation of common fixed points of finite family of k-strictly asymptotically pseudo-contractive mappings is proved in Banach spaces using the modified iteration process.

Highlights

Introduction and PreliminariesLet E be an arbitrary real Banach space and let J denote normalized duality mapping from E into 2E* given by such thatT n x T n y, j x y an x y1 1 k x Tnx y Tny (1)for all n N
The composite implicit iteration process introduced by Su and Li [J
A strong convergence theorem for approximation of common fixed points of finite family of k strictly asymptotically pseudo-contractive mappings is proved in Banach spaces using the modified iteration process

Summary

Introduction

Introduction and PreliminariesLet E be an arbitrary real Banach space and let J denote normalized duality mapping from E into 2E* given by such thatT n x T n y, j x y an x y1 1 k x Tnx y Tny (1)for all n N. A strong convergence theorem for approximation of common fixed points of finite family of k strictly asymptotically pseudo-contractive mappings is proved in Banach spaces using the modified iteration process. A mapping T : K K is called k-strictly asymptotically pseudocontractive with sequence an [1, ) , limn an 1 (see, for example [1]) if for all x, y K , there exists j x y J x y and a constant k [0,1)

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