Abstract and Applied Analysis
Volume 2010 (2010), Article ID 876819, 17 pages
doi:10.1155/2010/876819
Research Article

A Strong Convergence Theorem for a Common Fixed Point of Two Sequences of Strictly Pseudocontractive Mappings in Hilbert Spaces and Applications

Kasamsuk Ungchittrakool1,2

1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

Received 17 July 2010; Accepted 27 October 2010

Academic Editor: Chaitan Gupta

Copyright © 2010 Kasamsuk Ungchittrakool. 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

We prove a strong convergence theorem for a common fixed point of two sequences of strictly pseudocontractive mappings in Hilbert spaces. We also provide some applications of the main theorem to find a common element of the set of fixed points of a strict pseudocontraction and the set of solutions of an equilibrium problem in Hilbert spaces. The results extend and improve the recent ones announced by Marino and Xu (2007) and others.