Split equality fixed point problems for Lipchitz hemi-contractive mappings

Abstract

A very important general class of split feasiblity problem was introduced by Moudafi and Al-Shamas 13], in the case when the mappings are firmly nonexpansive defined on real Hilbert spaces. We propose in this paper a new Krasnoselskii’s-type algorithm to solve the problem in the more general case when the mappings are Lipschitz hemicontractive. We show that the proposed algorithm converges weakly to a solution of the problem. We also show that the iterative sequence obtained converges strongly to a solution of the problem under suitable compactness assumptions.