Taiwanese Journal of Mathematics

Some Modified Extragradient Methods for Common Solutions of Generalized Equilibrium Problems and Fixed Points of Nonexpansive Mappings

Jian-Wen Peng and Ngai-Ching Wong

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Abstract

In this paper, we introduce some new iterative schemes based on the extragradient method (and the hybrid method) for finding a common element of the set of solutions of a generalized equilibrium problem, the set of fixed points of a family of nonexpansive mappings, and the set of solutions of the variational inequality for a monotone, Lipschitz continuous mapping in Hilbert spaces. We obtain some strong convergence theorems and weak convergence theorems. The results in this paper generalize, improve and unify some well-known convergence theorems in the literature.

Article information

Source
Taiwanese J. Math., Volume 15, Number 1 (2011), 353-363.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406179

Digital Object Identifier
doi:10.11650/twjm/1500406179

Mathematical Reviews number (MathSciNet)
MR2780289

Zentralblatt MATH identifier
1228.47062

Subjects
Primary: 47J05: Equations involving nonlinear operators (general) [See also 47H10, 47J25] 47J25: Iterative procedures [See also 65J15] 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.

Keywords
generalized equilibrium problem extragradient method hybrid method nonexpansive mapping strong convergence weak convergence

Citation

Peng, Jian-Wen; Wong, Ngai-Ching. Some Modified Extragradient Methods for Common Solutions of Generalized Equilibrium Problems and Fixed Points of Nonexpansive Mappings. Taiwanese J. Math. 15 (2011), no. 1, 353--363. doi:10.11650/twjm/1500406179. https://projecteuclid.org/euclid.twjm/1500406179


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