International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 459085, 9 pages
http://dx.doi.org/10.1155/2011/459085
Research Article

Common Fixed-Point Problem for a Family Multivalued Mapping in Banach Space

Zhanfei Zuo

Department of Mathematics and Computer Science, Chongqing Three Gorges University, Wanzhou 404000, China

Received 11 December 2010; Revised 15 March 2011; Accepted 17 March 2011

Academic Editor: Vittorio Colao

Copyright © 2011 Zhanfei Zuo. 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

It is our purpose in this paper to prove two convergents of viscosity approximation scheme to a common fixed point of a family of multivalued nonexpansive mappings in Banach spaces. Moreover, it is the unique solution in 𝐹 to a certain variational inequality, where 𝐹 ∶ = ∩ ∞ 𝑛 = 0 𝐹 ( 𝑇 𝑛 ) stands for the common fixed-point set of the family of multivalued nonexpansive mapping { 𝑇 𝑛 } .