Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 390634, 10 pages
doi:10.1155/2009/390634
Research Article

Weak Contractions, Common Fixed Points, and Invariant Approximations

Nawab Hussain1 and Yeol Je Cho2

1Department of Mathematics, King Abdul Aziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, South Korea

Received 19 January 2009; Accepted 23 February 2009

Academic Editor: Charles E. Chidume

Copyright © 2009 Nawab Hussain and Yeol Je Cho. 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

The existence of common fixed points is established for the mappings, where T is (f,θ,L)-weak contraction on a nonempty subset of a Banach space. As application, some results on the invariant best approximation are proved. Our results unify and substantially improve several recent results given by some authors.