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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 513678, 25 pages
http://dx.doi.org/10.1155/2014/513678
Research Article

Strong and Weak Convergence Criteria of Composite Iterative Algorithms for Systems of Generalized Equilibria

1Department of Mathematics, Shanghai Normal University and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China
2Department of Food and Beverage Management, Vanung University, Chung-Li 320061, Taiwan
3Department of Information Management, Yuan Ze University, Chung-Li 32003, Taiwan
4Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, Taiwan
5Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

Received 20 January 2014; Accepted 12 February 2014; Published 25 March 2014

Academic Editor: Jen-Chih Yao

Copyright © 2014 Lu-Chuan Ceng 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 first introduce and analyze one iterative algorithm by using the composite shrinking projection method for finding a solution of the system of generalized equilibria with constraints of several problems: a generalized mixed equilibrium problem, finitely many variational inequalities, and the common fixed point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense and infinitely many nonexpansive mappings in a real Hilbert space. We prove a strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another iterative algorithm involving no shrinking projection method and derive its weak convergence under mild assumptions. Our results improve and extend the corresponding results in the earlier and recent literature.