全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

A New Iterative Method for Finding Common Solutions of a System of Equilibrium Problems, Fixed-Point Problems, and Variational Inequalities

DOI: 10.1155/2010/428293

Full-Text   Cite this paper   Add to My Lib

Abstract:

We introduce a new iterative scheme based on extragradient method and viscosity approximation method for finding a common element of the solutions set of a system of equilibrium problems, fixed point sets of an infinite family of nonexpansive mappings, and the solution set of a variational inequality for a relaxed cocoercive mapping in a Hilbert space. We prove strong convergence theorem. The results in this paper unify and generalize some well-known results in the literature. 1. Introduction Let be a real Hilbert space with inner product and induced norm . Let be a nonempty, closed, and convex subset of . Let be a countable family of bifunctions from to , where is the set of real numbers. Combettes and Hirstoaga [1] considered the following system of equilibrium problems: If is a singleton, problem (1.1) becomes the following equilibrium problem: The solutions set of (1.2) is denoted by . And clearly the solutions set of problem (1.1) can be written as . Problem (1.1) is very general in the sense that it includes, as special cases, optimization problems, variational inequalities, minimax problems, Nash equilibrium problem in noncooperative games, and others; see for instance, [1–4]. Recall that a mapping of a closed and convex subset into itself is nonexpansive if We denote fixed-points set of by . A mapping is called contraction if there exists a constant such that A bounded linear operator on is strongly positive, if there is a constant such that for all . Combettes and Hirstoaga [1] introduced an iterative scheme for finding a common element of the solutions set of problem (1.1) in a Hilbert space and obtained a weak convergence theorem. Peng and Yao [2] introduced a new viscosity approximation scheme based on the extragradient method for finding a common element in the solutions set of the problem (1.1), fixed-points set of an infinite family of nonexpansive mappings and the solutions set of the variational inequality for a monotone and Lipschitz continuous mapping in a Hilbert space and obtained a strong convergence theorem. Colao et al. [3] introduced an implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed-points of infinite family of nonexpansive mappings in a Hilbert space and obtained a strong convergence theorem. Saeidi [4] introduced some iterative algorithms for finding a common element of the solutions set of a system of equilibrium problems and of fixed-points set of a finite family and a left amenable semigroup of nonexpansive mappings in a Hilbert space and obtained some

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133