Article ID: | iaor201110507 |
Volume: | 51 |
Issue: | 4 |
Start Page Number: | 689 |
End Page Number: | 714 |
Publication Date: | Dec 2011 |
Journal: | Journal of Global Optimization |
Authors: | Kamraksa Uthai, Wangkeeree Rabian |
Keywords: | programming: multiple criteria |
In this paper, we introduce two iterative schemes (one implicit and one explicit) for finding a common element of the set of solutions of the generalized equilibrium problems and the set of all common fixed points of a nonexpansive semigroup in the framework of a real Hilbert space. We prove that both approaches converge strongly to a common element of such two sets. Such common element is the unique solution of a variational inequality, which is the optimality condition for a minimization problem. Furthermore, we utilize the main results to obtain two mean ergodic theorems for nonexpansive mappings in a Hilbert space. The results of this paper extend and improve the results of Li et al. (2009), Cianciaruso et al. (2010) and many others.