Faculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran.
In this paper, we discuss the existence and uniqueness of xed points for Banach and Kannan
contractions dened on modular spaces endowed with a graph. We do not impose the Δ2-condition
or the Fatou property on the modular spaces to give generalizations of some recent results. The
given results play as a modular version of metric xed point results.