International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 3, Pages 173-177
doi:10.1155/S0161171200003252

Approximating fixed points of nonexpansive mappings

Guimei Liu,1 Deng Lei,2 and Shenghong Li1

1Department of Mathematics, Zhejiang University, Zhejiang, 310027, China
2Department of Mathematics, Southwest China Normal University, Beibei, Chongqing 400715, China

Received 27 October 1998; Revised 19 April 1999

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a mapping S of the form S=α0I+α1T1+α2T2+⋯+αkTk, where αi≥0, α0>0, α1>0 and ∑i=0kαi=1. We show that the Picard iterates of S converge to a common fixed point of Ti(i=1,2,…,k)in a Banach space when Ti(i=1,2,…,k) are nonexpansive.