Iterative construction of fixed points of strictly pseudocontractive mappings

1 February 1991

journal article
research article
Published by Taylor & Francis in Applicable Analysis

Vol. 40 (2-3) , 67-72
https://doi.org/10.1080/00036819108839994

Abstract

Let (E, ‖ • ‖) be a smooth Banach space over the real field and A a nonempty closed bounded convex subset of E. Suppose T : A → A is a uniformly continuous strictly pseudocontractive selfmapping of A. Then, if [math001]satisfies [math001]the iteration process [math001] and [math001] converges strongly to the unique fixed point x of T. This is an improvement of a result of C.E. Chidume who established strong convergence of (x ⁿ to x in case E is L ^p or l ^p with [math001] making essential use of the inepuality [math001] which is kown to hold in these spaces for all x and y

Keywords

This publication has 3 references indexed in Scilit:

Weak Parallelogram Laws for Banach Spaces
Canadian Mathematical Bulletin, 1976
Zeros of accretive operators
manuscripta mathematica, 1974
Differential equations on closed subsets of a Banach space
Transactions of the American Mathematical Society, 1973