Strong Convergence of a New Iterative Method for Infinite Family of Generalized Equilibrium and Fixed-Point Problems of Nonexpansive Mappings in Hilbert Spaces

Fixexd point theory and applications

Baohua Guo¹  Shenghua Wang² 

[1] Department of Mathematics and Physics, North China Electric Power University, Baoding, China;National Engineering Laboratory for Biomass Power Generation Equipment, North China Electric Power University, Baoding, China

关键词: Hilbert Space;    Variational Inequality;    Equilibrium Problem;    Nonexpansive Mapping;    Iterative Scheme;   

DOI  :  10.1155/2011/392741

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We introduce an iterative algorithm for finding a common element of the set of solutions of an infinite family of equilibrium problems and the set of fixed points of a finite family of nonexpansive mappings in a Hilbert space. We prove some strong convergence theorems for the proposed iterative scheme to a fixed point of the family of nonexpansive mappings, which is the unique solution of a variational inequality. As an application, we use the result of this paper to solve a multiobjective optimization problem. Our result extends and improves the ones of Colao et al. (2008) and some others.

【 授权许可】

CC BY