Open Access

Weak Convergence Theorems of Three Iterative Methods for Strictly Pseudocontractive Mappings of Browder-Petryshyn Type

Fixed Point Theory and Applications20082008:672301

https://doi.org/10.1155/2008/672301

Received: 25 September 2007

Accepted: 28 February 2008

Published: 13 March 2008

Abstract

Let be a real -uniformly smooth Banach space which is also uniformly convex (e.g., or spaces , and a nonempty closed convex subset of . By constructing nonexpansive mappings, we elicit the weak convergence of Mann's algorithm for a -strictly pseudocontractive mapping of Browder-Petryshyn type on in condition thet the control sequence is chosen so that (i) (ii) , where . Moreover, we consider to find a common fixed point of a finite family of strictly pseudocontractive mappings and consider the parallel and cyclic algorithms for solving this problem. We will prove the weak convergence of these algorithms.

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Authors’ Affiliations

(1)
School of Mathematics and Physics, North China Electric Power University

Copyright

© Y. Zhang and Y. Guo. 2008

This article is published under license to BioMed Central Ltd. 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.