Approximating fixed point of({\lambda},{\rho})-firmly nonexpansive mappings in modular function spaces

TL;DR

This paper extends the concept of {\

Contribution

It introduces ({\lambda},{\rho})-firmly nonexpansive mappings in modular function spaces and develops an iterative process to approximate their fixed points.

Findings

Established convergence of the iterative process in modular spaces

Provided an example validating the theoretical results

Extended fixed point approximation methods beyond Banach spaces

Abstract

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