The Contraction Principle for Multivalued Mappings on a Modular Metric Space with a Graph
Printed: Mar 2016
We study the existence of fixed points for contraction multivalued
mappings in modular metric spaces endowed with a graph. 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. This paper can
be seen as a generalization of Nadler's and Edelstein's fixed
point theorems to modular metric spaces endowed with a graph.
fixed point theory, modular metric spaces, multivalued contraction mapping, connected digraph.
47H09 - Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc.
46B20 - Geometry and structure of normed linear spaces
47H10 - Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]
47E10 - unknown classification 47E10