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

作者：Jung Jong Soo^*

来源：Journal of Inequalities and Applications, 2011, 1-23.

DOI：10.1186/1029-242X-2011-51

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

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.

• 出版日期2011