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# The Contraction Principle for Multivalued Mappings on a Modular Metric Space with a Graph

Published:2015-05-21
Printed: Mar 2016
• Monther Rashed Alfuraidan,
Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
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## Abstract

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.
 Keywords: fixed point theory, modular metric spaces, multivalued contraction mapping, connected digraph.
 MSC Classifications: 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

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