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1. A Hybrid Extragradient-Like Method for Variational Inequalities, Equilibrium Problems, and an Infinitely Family of Strictly Pseudocontractive Mappings.

Author

Yaqin Wang and Xiaoli Fang

Subjects
*VARIATIONAL inequalities (Mathematics), *PROBLEM solving, *CONTRACTIONS (Topology), *MATHEMATICAL mappings, *STOCHASTIC convergence, *HILBERT space, *ITERATIVE methods (Mathematics), *ALGORITHMS
Abstract

The purpose of this paper is to consider a new scheme by the hybrid extragradient-like method for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a variational inequality, and the set of fixed points of an infinitely family of strictly pseudocontractive mappings in Hilbert spaces. Then, we obtain a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm. Our results extend and improve the results of Issara Inchan 2010 and many others. [ABSTRACT FROM AUTHOR]

Published
2012
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2. Some new algorithms for solving mixed equilibrium problems

Author

Yao, Yonghong, Noor, Muhammad Aslam, Liou, Yeong-Cheng, and Kang, Shin Min

Subjects
*ALGORITHMS, *PROBLEM solving, *HILBERT space, *VARIATIONAL inequalities (Mathematics), *MATHEMATICAL proofs, *STOCHASTIC convergence
Abstract

Abstract: In this paper, we suggest and analyze two projection methods (one implicit and one explicit) for finding a particular solution of a mixed equilibrium problem in a real Hilbert space. Furthermore, we prove that the proposed projection methods converge strongly to a particular solution of the mixed equilibrium problem. [ABSTRACT FROM AUTHOR]

Published
2010
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