The split equilibrium problem and common fixed points of two relatively quasi-nonexpansive mappings in Banach spaces

Abstract

© 2019 Yokohama Publications. All rights reserved. In this paper, we prove a strong convergence theorem for finding a common element of the solution set of the split equilibrium problem and a common fixed points set of two relatively quasi-nonexpansive mappings in Banach spaces. Furthermore, we also prove a weak convergence theorem for the split equilibrium problem and a common fixed points set of two relatively nonexpansive mappings. Consequently, our main results can be applied to some equilibrium problems in Banach spaces.