Inertial reflected Krasnosel’ski-Mann iteration with applications to monotone inclusion problems

Abstract

This paper studies an inertial reflected method for the approximation of fixed points (assuming existence) of nonexpansive mappings in Hilbert spaces. The proposed method is a combination of Krasnosel'ski-Mann iteration, inertial extrapolation step and reflected step. The aim is to improve and complement various versions of inertial Krasnosel'ski-Mann iterations and the recently proposed reflected Krasnosel'ski-Mann iteration in the literature for approximating fixed points of nonexpansive mappings in Hilbert spaces. Some applications to problems of finding zeros of the sum of monotone operators are given. Finally, numerical simulations including image restoration problems are performed using standard test examples to show the superiority of our proposed method.