Strong convergence theorems for a generalized mixed equilibrium problem and variational inequality problems

Fixexd point theory and applications

Jae Ug Jeong¹ 

[1] Department of Mathematics, Dongeui University, Busan, South Korea

关键词: fixed point;    inverse strongly monotone mapping;    variational inequality;    equilibrium problem;   

DOI  :  10.1186/1687-1812-2013-65

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, a new iterative scheme based on the extragradient-like method for finding a common element of the set of common fixed points of a finite family of nonexpansive mappings, the set of solutions of variational inequalities for a strongly positive linear bounded operator and the set of solutions of a mixed equilibrium problem is proposed. A strong convergence theorem for this iterative scheme in Hilbert spaces is established. Our results extend recent results announced by many others. MSC:49J30, 49J40, 47J25, 47H09.

【 授权许可】

CC BY