An iterative scheme for split equality equilibrium problems and split equality hierarchical fixed point problem

Advances in Difference Equations

Monairah Alansari¹ 

[1] Department of Mathematics, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia;

关键词: Split equality equilibrium problem;    Split equality hierarchical fixed point problem;    Simultaneous hybrid projected subgradient-proximal iterative scheme;    Quasinonexpansive mapping;    Pseudomonotone bifunction;    47H09;    47J20;    49J30;    90C25;   

DOI  :  10.1186/s13662-021-03384-y

来源: Springer

【 摘 要 】

This paper deals with a split equality equilibrium problem for pseudomonotone bifunctions and a split equality hierarchical fixed point problem for nonexpansive and quasinonexpansive mappings. We suggest and analyze an iterative scheme where the stepsizes do not depend on the operator norms, the so-called simultaneous projected subgradient-proximal iterative scheme for approximating a common solution of the split equality equilibrium problem and the split equality hierarchical fixed point problem. Further, we prove a weak convergence theorem for the sequences generated by this scheme. Furthermore, we discuss some consequences of the weak convergence theorem. We present a numerical example to justify the main result.

【 授权许可】

CC BY