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
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 Guimei Liu et al. 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.