Fixed points for Banach and Kannan contractions in modular spaces with a graph

Abstract

In this paper, we discuss the existence and uniqueness of xed points for Banach and Kannan<br />contractions de ned on modular spaces endowed with a graph. We do not impose the Δ2-condition<br />or the Fatou property on the modular spaces to give generalizations of some recent results. The<br />given results play as a modular version of metric xed point results.