Iterative algorithm for a family of split equilibrium problems and fixed point problems in Hilbert spaces with applications

Fixexd point theory and applications

Yeol Je Cho¹  Shenghua Wang²  Xiaoying Gong³  Afrah AN Abdou⁴ 

[1] Department of Mathematics Education and RINS, Gyeongsang National University, Jinju, Korea;Department of Mathematics and Physics, North China Electric Power University, Baoding, China;Department of Mathematics and Sciences, Shijiazhuang University of Economics, Shijiazhuang, China;Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

关键词: split equilibrium problem;    nonexpansive mapping;    split feasible solution problem;    Hilbert space;    47H10;    54H25;    65J15;    90C30;   

DOI  :  10.1186/s13663-015-0475-2

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we propose an iterative algorithm and, by using the proposed algorithm, prove some strong convergence theorems for finding a common element of the set of solutions of a finite family of split equilibrium problems and the set of common fixed points of a countable family of nonexpansive mappings in Hilbert spaces. An example is given to illustrate the main result of this paper. As an application, we construct an algorithm to solve an optimization problem.

【 授权许可】

CC BY