A shrinking projection approximant for the split equilibrium problems and fixed point problems in Hilbert spaces

TL;DR

This paper introduces a new iterative algorithm using the shrinking projection method to find common solutions to split equilibrium problems and fixed point problems in Hilbert spaces, with proven strong convergence.

Contribution

It develops a novel approximation method that extends existing results for solving split equilibrium and fixed point problems in Hilbert spaces.

Findings

The algorithm converges strongly in Hilbert spaces.

It unifies solutions for split equilibrium and fixed point problems.

The method improves upon previous convergence results.

Abstract

This work is devoted to establish the strong convergence results of an iterative algorithm generated by the shrinking projection method in Hilbert spaces. The proposed approximation sequence is used to find a common element in the set of solutions of a finite family of split equilibrium problems and the set of common fixed points of a finite family of total asymptotically strict pseudo contractions in such setting. The results presented in this paper improve and extend some recent corresponding results in the literature.