Fixed Points for Banach and Kannan Contractions in Modular Spaces with a Graph

TL;DR

This paper investigates fixed point existence and uniqueness for Banach and Kannan contractions within modular spaces equipped with a graph, without relying on traditional conditions like $ riangle_2$ or Fatou property.

Contribution

It introduces new fixed point results for contractions in modular spaces with a graph, removing the need for $ riangle_2$-condition or Fatou property assumptions.

Findings

Established fixed point existence for Banach contractions in modular spaces with a graph.

Proved uniqueness of fixed points under Kannan contractions in the same setting.

Extended fixed point theory by removing common restrictive conditions.

Abstract

In this paper, we discuss the existence and uniqueness of fixed points for Banach and Kannan $\widetilde G$-$\rho$-contractions defined on modular spaces endowed with a graph without using the $\Delta_2$-condition or the Fatou property.