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

Document Type : Research Paper


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 fixed points for Banach and Kannan contractions defined on modular spaces endowed with a graph. We do not impose the $\Delta_2$-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 fixed point results.


  • Receive Date: 11 August 2013
  • Revise Date: 04 March 2014
  • Accept Date: 21 March 2014