An inertial Mann-like algorithm for fixed points of nonexpansive mappings in Hilbert spaces

Abstract

. In this paper, we investigate an inertial Mann-like algorithm for fixed points of nonexpansive mappings in Hilbert spaces and obtain strong convergence results under some mild assumptions. Based on this, we derive a forward-backward algorithm involving Tikhonov regularization terms, which converges strongly to the solution of the monotone inclusion problem. We demonstrate the advantages of our algorithms comparing with some existing ones in the literature via split feasibility problem, variational inequality problem and signal recovery problem.