A New Approach to Study Fixed Point of Multivalued Mappings in Modular Metric Spaces and Applications

Dilip Jain, Anantachai Padcharoen, Poom Kumam and Dhananjay Gopal
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Dilip Jain: Department of Applied Mathematics & Humanities, S.V. National Institute of Technology, Surat-395007 Gujarat, India
Anantachai Padcharoen: Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
Poom Kumam: Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
Dhananjay Gopal: Department of Applied Mathematics & Humanities, S.V. National Institute of Technology, Surat-395007 Gujarat, India

Mathematics, 2016, vol. 4, issue 3, 1-9

Abstract: The purpose of this paper is to present a new approach to study the existence of fixed points for multivalued F -contraction in the setting of modular metric spaces. In establishing this connection, we introduce the notion of multivalued F -contraction and prove corresponding fixed point theorems in complete modular metric space with some specific assumption on the modular. Then we apply our results to establish the existence of solutions for a certain type of non-linear integral equations.

Keywords: Keywords; fixed point; multivalued F -contractive; modular metric space; non-linear integral equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2016
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