A general composite iterative method for generalized mixed equilibrium problems, variational inequality problems and optimization problems

Journal of inequalities and applications

Jong Soo Jung¹ 

关键词: generalized mixed equilibrium problem;    fixed point;    nonexpansive mapping;    inverse-strongly monotone mapping;    variational inequality;    optimization problem;    metric projection;    strongly positive bounded linear operator;   

DOI  :  10.1186/1029-242X-2011-51

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, we introduce a new general composite iterative scheme for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality problem for an inverse-strongly monotone mapping in Hilbert spaces. It is shown that the sequence generated by the proposed iterative scheme converges strongly to a common element of the above three sets under suitable control conditions, which solves a certain optimization problem. The results of this article substantially improve, develop, and complement the previous well-known results in this area. 2010 Mathematics Subject Classifications: 49J30; 49J40; 47H09; 47H10; 47J20; 47J25; 47J05; 49M05.

【 授权许可】

CC BY