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.

Keywords

• weak convergence
• inertial iteration
• nonexpansive operator
• enriched non-expansive operator
• hilbert space
• primary 46g05, 46l05
• secondary 47a30, 47b47