Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 462489, 12 pages
Research Article

Strong Convergence Theorems for Countable Lipschitzian Mappings and Its Applications in Equilibrium and Optimization Problems

1Department of Fundamental, Tianjin Institute of Urban Construction, Tianjin 300384, China
2Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China

Received 21 October 2008; Revised 20 December 2008; Accepted 5 March 2009

Academic Editor: Naseer Shahzad

Copyright © 2009 Liping Yang and Yongfu Su. 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.


The purpose of this paper is to propose a modified hybrid method in mathematical programming and to obtain some strong convergence theorems for common fixed points of a countable family of Lipschitzian mappings. Further, we apply our results to solve the equilibrium and optimization problems. The results of this paper improved and extended the results of W. Nilsrakoo and S. Saejung (2008) and some others in some respects.