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

被引：0
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作者：
Shenghua Wang
Baohua Guo
机构：
[1] North China Electric Power University,National Engineering Laboratory for Biomass Power Generation Equipment
[2] North China Electric Power University,Department of Mathematics and Physics
来源：
Fixed Point Theory and Applications | / 2011卷
关键词：
Hilbert Space; Variational Inequality; Equilibrium Problem; Nonexpansive Mapping; Iterative Scheme;
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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.
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