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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 436069, 27 pages
http://dx.doi.org/10.1155/2014/436069
Research Article

Hybrid Extragradient Method with Regularization for Convex Minimization, Generalized Mixed Equilibrium, Variational Inequality and Fixed Point Problems

1Department of Mathematics, Shanghai Normal University and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China
2Department of Finance, Tainan University of Technology, No. 529, Zhongzheng Road, YongKang District, Tainan 71002, Taiwan

Received 15 October 2013; Revised 25 November 2013; Accepted 25 November 2013; Published 4 February 2014

Academic Editor: Erdal Karapınar

Copyright © 2014 Lu-Chuan Ceng and Juei-Ling Ho. 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 two iterative algorithms by the hybrid extragradient method with regularization for finding a common element of the set of solutions of the minimization problem for a convex and continuously Fréchet differentiable functional, the set of solutions of finite generalized mixed equilibrium problems, the set of solutions of finite variational inequalities for inverse strong monotone mappings and the set of fixed points of an asymptotically -strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove some strong and weak convergence theorems for the proposed iterative algorithms under mild conditions.