Strong Convergence Theorems for a Generalized Equilibrium Problem with a Relaxed Monotone Mapping and a Countable Family of Nonexpansive Mappings in a Hilbert Space

Fixexd point theory and applications

Fuhai Wang¹  Giuseppe Marino²  Shenghua Wang³ 

[1] della Calabria, Arcavacata di Rende, Italy;Dipartimento di Matematica, UniversitáSchool of Applied Mathematics and Physics, North China Electric Power University, Baoding, China

关键词: Hilbert Space;    Variational Inequality;    Iterative Method;    Equilibrium Problem;    Monotone Mapping;   

DOI  :  10.1155/2010/230304

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We introduce a new iterative method for finding a common element of the set of solutions of a generalized equilibrium problem with a relaxed monotone mapping and the set of common fixed points of a countable family of nonexpansive mappings in a Hilbert space and then prove that the sequence converges strongly to a common element of the two sets. Using this result, we prove several new strong convergence theorems in fixed point problems, variational inequalities, and equilibrium problems.

【 授权许可】

CC BY