Weak convergence theorems for inertial Krasnoselskii-Mann iterations in the class of enriched nonexpansive operators in Hilbert spaces

Abstract In this paper, we present some results about the aproximation of fixed points of nonexpansive and enriched nonexpansive operators. In order to approximate the fixed points of enriched nonexpansive mappings, we use the Krasnoselskii-Mann iteration for which we prove weak convergence theorem and the theorem which offers the convergence rate analysis. Our results in this paper extend some classical convergence theorems from the literature from the case of nonexpansive mappings to that of enriched nonexpansive mappings. One of our contributions is that the convergence analysis and rate of convergence results are obtained using conditions which appear not complicated and restrictive as assumed in other previous related results in the literature.