Abstract and Applied Analysis
Volume 2012 (2012), Article ID 435790, 6 pages
http://dx.doi.org/10.1155/2012/435790
Research Article

Convergence Theorems for Infinite Family of Multivalued Quasi-Nonexpansive Mappings in Uniformly Convex Banach Spaces

Aunyarat Bunyawat1,2 and Suthep Suantai1,2

1Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

Received 13 December 2011; Accepted 6 January 2012

Academic Editor: Simeon Reich

Copyright © 2012 Aunyarat Bunyawat and Suthep Suantai. 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 an iterative method for finding a common fixed point of a countable family of multivalued quasi-nonexpansive mapping {Ti} in a uniformly convex Banach space. We prove that under certain control conditions, the iterative sequence generated by our method is an approximating fixed point sequence of each Ti. Some strong convergence theorems of the proposed method are also obtained for the following cases: all Ti are continuous and one of Ti is hemicompact, and the domain K is compact.