Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 15, Number 1 (2011), 353-363.
Some Modified Extragradient Methods for Common Solutions of Generalized Equilibrium Problems and Fixed Points of Nonexpansive Mappings
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.
Taiwanese J. Math., Volume 15, Number 1 (2011), 353-363.
First available in Project Euclid: 18 July 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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.
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