A Study of a Nonlinear Ordinary Differential Equation in Modular Function Spaces Endowed with a Graph

In this paper, we prove by means of a fixed-point theorem an existence result of the Cauchy problem associated to an ordinary differential equation in modular function spaces endowed with a reflexive convex digraph

Some Fixed Point Theorems in Modular Function Spaces Endowed with a Graph

The aim of this paper is to give fixed point theorems for G-monotone ρ-nonexpansive mappings over ρ-compact or ρ-a.e. compact sets in modular function spaces endowed with a reflexive digraph not necessarily transitive. Examples are given to support our work

Common Fixed-Point Theorems in Modular Function Spaces Endowed with Reflexive Digraph

The purpose of this work is to extend the Knaster–Tarski fixed-point theorem to the wider field of reflexive digraph. We give also a DeMarr-type common fixed-point theorem in this context. We then explore some interesting applications of the obtained results in modular function spaces