The Fibonacci–Mann iteration for monotone asymptotically pointwise nonexpansive mappings

Abstract

In this work, we investigate the convergence of the Fibonacci–Mann iteration associated with a monotone asymptotic pointwise nonexpansive mapping defined in a modular function space. The first main result deals with the modular convergence of such iteration when the mapping is assumed to be compact. Relaxing the compactness assumption, we obtain a $$\rho $$ -a.e. convergence of the iteration. These two results are similar to the main conclusions of the original work of Schu.