Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 407651, 26 pages
doi:10.1155/2010/407651
Research Article

Approximation of Common Fixed Points of a Countable Family of Relatively Nonexpansive Mappings

Daruni Boonchari1 and Satit Saejung2

1Department of Mathematics, Mahasarakham University, Maha Sarakham 44150, Thailand
2Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand

Received 22 June 2009; Revised 20 October 2009; Accepted 21 November 2009

Academic Editor: Tomonari Suzuki

Copyright © 2010 Daruni Boonchari and Satit Saejung. 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 introduce two general iterative schemes for finding a common fixed point of a countable family of relatively nonexpansive mappings in a Banach space. Under suitable setting, we not only obtain several convergence theorems announced by many authors but also prove them under weaker assumptions. Applications to the problem of finding a common element of the fixed point set of a relatively nonexpansive mapping and the solution set of an equilibrium problem are also discussed.