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Journal of Applied Mathematics
Volume 2012, Article ID 865810, 20 pages
http://dx.doi.org/10.1155/2012/865810
Research Article

On Variational Inclusion and Common Fixed Point Problems in q-Uniformly Smooth Banach Spaces

Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

Received 9 June 2012; Accepted 18 August 2012

Academic Editor: Alicia Cordero

Copyright © 2012 Yanlai Song et al. 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 a general iterative algorithm for finding a common element of the common fixed-point set of an infinite family of -strict pseudocontractions and the solution set of a general system of variational inclusions for two inverse strongly accretive operators in a q-uniformly smooth Banach space. Then, we prove a strong convergence theorem for the iterative sequence generated by the proposed iterative algorithm under very mild conditions. The methods in the paper are novel and different from those in the early and recent literature. Our results can be viewed as the improvement, supplementation, development, and extension of the corresponding results in some references to a great extent.