## Taiwanese Journal of Mathematics

### A NEW HYBRID-EXTRAGRADIENT METHOD FOR GENERALIZED MIXED EQUILIBRIUM PROBLEMS, FIXED POINT PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS

#### Abstract

In this paper, we introduce a new iterative scheme based on the hybrid method and the extragradient method for finding a common element of the set of solutions of a generalized mixed equilibrium problem and the set of fixed points of a nonexpansive mapping and the set of the variational inequality for a monotone, Lipschitz-continuous mapping. We obtain a strong convergence theorem for the sequences generated by these processes in Hilbert spaces. Based on this result, we also get some new and interesting results. The results in this paper generalize, extend and unify some well-known strong convergence theorems in the literature.

#### Article information

Source
Taiwanese J. Math., Volume 12, Number 6 (2008), 1401-1432.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500405033

Digital Object Identifier
doi:10.11650/twjm/1500405033

Mathematical Reviews number (MathSciNet)
MR2444865

Zentralblatt MATH identifier
1185.47079

#### Citation

Peng, Jian-Wen; Yao, Jen-Chih. A NEW HYBRID-EXTRAGRADIENT METHOD FOR GENERALIZED MIXED EQUILIBRIUM PROBLEMS, FIXED POINT PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS. Taiwanese J. Math. 12 (2008), no. 6, 1401--1432. doi:10.11650/twjm/1500405033. https://projecteuclid.org/euclid.twjm/1500405033

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