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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 384108, 18 pages
http://dx.doi.org/10.1155/2012/384108
Research Article

Weak Convergence Theorems for Strictly Pseudocontractive Mappings and Generalized Mixed Equilibrium Problems

Department of Mathematics, Dong-A University, Busan 604-714, Republic of Korea

Received 15 February 2012; Accepted 6 April 2012

Academic Editor: Yonghong Yao

Copyright © 2012 Jong Soo Jung. 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 new iterative method for finding a common element of the set of fixed points of a strictly pseudocontractive mapping, the set of solutions of a generalized mixed equilibrium problem, and the set of solutions of a variational inequality problem for an inverse-strongly-monotone mapping in Hilbert spaces and then show that the sequence generated by the proposed iterative scheme converges weakly to a common element of the above three sets under suitable control conditions. The results in this paper substantially improve, develop, and complement the previous well-known results in this area.