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

Jian-Wen Peng | Zendy; SoonYi Wu | Zendy; JenChih Yao | Zendy

Open Access

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

Author(s) -

Jian-Wen Peng,

SoonYi Wu,

JenChih Yao

Publication year - 2010

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2010/428293

Subject(s) - variational inequality , mathematics , hilbert space , fixed point , convergence (economics) , scheme (mathematics) , iterative method , set (abstract data type) , point (geometry) , fixed point theorem , mathematical optimization , mathematical analysis , computer science , geometry , economics , programming language , economic growth

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

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