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International Journal of Mathematics and Mathematical Sciences
Volume 16, Issue 1, Pages 81-86
http://dx.doi.org/10.1155/S0161171293000092

Approximating fixed points of nonexpansive and generalized nonexpansive mappings

Department of Mathematics, Indian Institute of Technology, Kharagpur, India

Received 20 May 1991; Revised 15 November 1991

Copyright © 1993 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

In this paper we consider a mapping S of the form S=α0I+α1T+α2T2++αKTK, where αi0. α1>0 with i=0kαi=1, and show that in a uniformly convex Banach space the Picard iterates of S converge to a fixed point of T when T is nonexpansive or generalized nonexpansive or even quasinonexpansive.