On the convergence of an implicit and relaxed Krasnoselskii-Mann type process for nonexpansive mappings

Abstract

In this paper, we answer a question raised by Hong-Kun Xu in [14] about the weak convergence of a generalized semi-implicit relaxed version of the Krasnoselskii-Mann process for nonexpansive mappings. The stability of this process is then studied, and some numerical experiments are provided in order to measure the effect of the process parameters on the convergence speed.