Open Access

A General Iterative Method for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

Fixed Point Theory and Applications20082007:095412

DOI: 10.1155/2007/95412

Received: 14 May 2007

Accepted: 18 September 2007

Published: 28 January 2008

Abstract

We introduce a general iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Our results improve and extend the corresponding ones announced by S. Takahashi and W. Takahashi in 2007, Marino and Xu in 2006, Combettes and Hirstoaga in 2005, and many others.

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Authors’ Affiliations

(1)
Department of Mathematics, Tianjin Polytechnic University
(2)
Department of Mathematics, Shijiazhuang University
(3)
Department of Mathematics, Gyeongsang National University

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Copyright

© Meijuan Shang et al. 2007

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.