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

抄録

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].