Journal of Applied Mathematics
Volume 2013 (2013), Article ID 926078, 8 pages
Research Article

Viscosity Approximation Methods and Strong Convergence Theorems for the Fixed Point of Pseudocontractive and Monotone Mappings in Banach Spaces

College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China

Received 22 January 2013; Revised 26 May 2013; Accepted 27 May 2013

Academic Editor: Filomena Cianciaruso

Copyright © 2013 Yan Tang. 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.


Suppose that is a nonempty closed convex subset of a real reflexive Banach space which has a uniformly Gateaux differentiable norm. A viscosity iterative process is constructed in this paper. A strong convergence theorem is proved for a common element of the set of fixed points of a finite family of pseudocontractive mappings and the set of solutions of a finite family of monotone mappings. And the common element is the unique solution of certain variational inequality. The results presented in this paper extend most of the results that have been proposed for this class of nonlinear mappings.