Open Access

Weak and Strong Convergence Theorems of an Implicit Iteration Process for a Countable Family of Nonexpansive Mappings

  • Kittikorn Nakprasit1,
  • Weerayuth Nilsrakoo2 and
  • Satit Saejung1Email author
Fixed Point Theory and Applications20082008:732193

https://doi.org/10.1155/2008/732193

Received: 22 July 2008

Accepted: 18 November 2008

Published: 26 November 2008

Abstract

Using the implicit iteration and the hybrid method in mathematical programming, we prove weak and strong convergence theorems for finding common fixed points of a countable family of nonexpansive mappings in a real Hilbert space. Our results include many convergence theorems by Xu and Ori (2001) and Zhang and Su (2007) as special cases. We also apply our method to find a common element to the set of fixed points of a nonexpansive mapping and the set of solutions of an equilibrium problem. Finally, we propose an iteration to obtain convergence theorems for a continuous monotone mapping.

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Authors’ Affiliations

(1)
Department of Mathematics, Khon Kaen University
(2)
Department of Mathematics, Statistics and Computer, Ubon Rajathanee University

Copyright

© Kittikorn Nakprasit et al. 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.