WEAK AND STRONG CONVERGENCE OF AN IMPLICIT ITERATION PROCESS FOR A FINITE FAMILY OF NONEXPANSIVE MAPPINGS

SORNSAK THIANWAN; SUTHEP SUANTAI

doi:10.32219/isms.66.1_73

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Keywords: Implicit iteration process, weak and strong convergence, nonexpansive mappings, Opial condition, Kadec-Klee property, condition (B), semi-compact, common fixed points

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2007 Volume 66 Issue 1 Pages 73-81

DOI https://doi.org/10.32219/isms.66.1_73

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Abstract

The purpose of this paper is to study weak and strong convergence of a new implicit iteration process to a common fixed point for a finite family of nonexpansive mappings in a uniformly convex Banach space. The results obtained in this paper extend and improve the corresponding results of [C. E. Chidume, N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62 (2005) 1149-1156; H.K. Xu, R. Ori, An implicit iterative process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001) 767-773].

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