Approximating fixed point of(λ,ρ)-firmly nonexpansive mappings in modular function spaces

Abstract

In this paper, we first introduce an iterative process in modular function spaces and then extend the idea of a λ-firmly nonexpansive mapping from Banach spaces to modular function spaces. We call such mappings as (λ,ρ)-firmly nonexpansive mappings. We incorporate the two ideas to approximate fixed points of (λ,ρ)-firmly nonexpansive mappings using the above mentioned iterative process in modular function spaces. We give an example to validate our results.