Journal of Applied Mathematics
Volume 2012 (2012), Article ID 308791, 18 pages
http://dx.doi.org/10.1155/2012/308791
Research Article

Strong Convergence to Solutions of Generalized Mixed Equilibrium Problems with Applications

Prasit Cholamjiak,1,2 Suthep Suantai,2,3 and Yeol Je Cho4

1School of Science, University of Phayao, Phayao 56000, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand
3Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
4Department of Mathematics Education and the RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea

Received 21 October 2011; Accepted 23 November 2011

Academic Editor: Yonghong Yao

Copyright © 2012 Prasit Cholamjiak 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 Halpern-type iteration for a generalized mixed equilibrium problem in uniformly smooth and uniformly convex Banach spaces. Strong convergence theorems are also established in this paper. As applications, we apply our main result to mixed equilibrium, generalized equilibrium, and mixed variational inequality problems in Banach spaces. Finally, examples and numerical results are also given.