Fixed points of multivalued contraction mappings in modular metric spaces

The purpose of this paper is to study the existence of fixed points for contractive-type multivalued maps in the setting of modular metric spaces. 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 investigate the existence of fixed points of multivalued modular contractive mappings in modular metric spaces. Consequently, our results either generalize or improve fixed point results of Nadler (Pac. J. Math. 30:475-488, 1969) and Edelstein (Proc. Am. Math. Soc. 12:7-10, 1961). MSC: Primary 47H09; secondary 46B20; 47H10; 47E10.