International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 1, Pages 81-86
doi: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 M. Maiti and B. Saha. 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 αi≥0. 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.