Iterative algorithms of common solutions for a hierarchical fixed point problem, a system of variational inequalities, and a split equilibrium problem in Hilbert spaces

Journal of inequalities and applications

Yali Zhao¹  Xin Liu¹  Ruonan Sun¹ 

[1] School of Mathematical Science, Bohai University, 121013, Liaoning, Jinzhou, China;

关键词: Hierarchical fixed point problem;    Split equilibrium problem;    System of variational inequalities;    Iterative algorithm;    Convergence;    49J30;    47H09;    47J20;   

DOI  :  10.1186/s13660-021-02645-4

来源: Springer

【 摘 要 】

In this paper, we suggest and analyze an iterative algorithm to approximate a common solution of a hierarchical fixed point problem for nonexpansive mappings, a system of variational inequalities, and a split equilibrium problem in Hilbert spaces. Under some suitable conditions imposed on the sequences of parameters, we prove that the sequence generated by the proposed iterative method converges strongly to a common element of the solution set of these three kinds of problems. The results obtained here extend and improve the corresponding results of the relevant literature.

【 授权许可】

CC BY