Modified S-Iteration process for solving equilibrium problem and fixed point problem of multi-valued relatively nonexpansive mappings in a real Banach space
Optimization Eruditorum, Volume 3, Issue 2, August 2026, Pages 108–126
OLUWATOSIN TEMITOPE MEWOMO
Department of Mathematics, Tarleton State University, Stephenville, Texas, United States
ADEOLU TAIWO
Department of Mathematics, Arizona Western College, Yuma, Arizona, United States
TIMILEHIN OPEYEMI ALAKOYA
School of Mathematics and Physics, Queen’s University Belfast, Belfast, United Kingdom
Abstract
We study the problem of finding the common element of the solution set of equilibrium problem and fixed point set of multi-valued relatively nonexpansive mappings in uniformly convex and uniformly smooth Banach space without the assumption of weak sequential continuity of the normalized duality mapping. We propose a modified S-iteration process for solving the problem and prove a strong convergence theorem. We apply our results to variational inequality and fixed point problems. Two numerical examples are presented to illustrate the performance of our method as well as comparing it with some related methods in the literature. Our main result extends and generalizes many existing results in the literature.
Cite this Article as
O. T. Mewomo, A. Taiwo and T. O. Alakoya, Modified S-Iteration process for solving equilibrium problem and fixed point problem of multi-valued relatively nonexpansive mappings in a real Banach space, Optimization Eruditorum, 3(2), 108–126, 2026