Fixed points of Kannan maps in modular metric spaces

Abstract

The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. In this paper we study the existence of fixed points for contractive and nonexpansive Kannan maps in the setting of modular metric spaces.These are related to the successive approximations of fixed points (via orbits) which converge to the fixed points in the modular sense, which is weaker than the metric convergence.

Keywords

• fixed point
• kannan contraction mapping
• kannan nonexpansive mapping
• modular metric spaces