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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 637324, 27 pages
Research Article

Multistep Hybrid Iterations for Systems of Generalized Equilibria with Constraints of Several Problems

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

Received 24 January 2014; Accepted 11 February 2014; Published 8 May 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.


We first introduce and analyze one multistep iterative algorithm by hybrid shrinking projection method for finding a solution of the system of generalized equilibria with constraints of several problems: the generalized mixed equilibrium problem, finitely many variational inclusions, the minimization problem for a convex and continuously Fréchet differentiable functional, and the fixed-point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another multistep iterative algorithm involving no shrinking projection method and derive its weak convergence under mild assumptions.