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Mathematics 2016, 4(3), 51; doi:10.3390/math4030051

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

1
Department of Applied Mathematics & Humanities, S.V. National Institute of Technology, Surat-395007 Gujarat, India
2
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
*
Author to whom correspondence should be addressed.
Academic Editor: Pasquale Vetro
Received: 5 June 2016 / Revised: 28 July 2016 / Accepted: 1 August 2016 / Published: 8 August 2016
(This article belongs to the Special Issue Fixed Point Theorems and Applications)
View Full-Text   |   Download PDF [241 KB, uploaded 8 August 2016]

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. View Full-Text
Keywords: Keywords; fixed point; multivalued F-contractive; modular metric space; non-linear integral equations Keywords; fixed point; multivalued F-contractive; modular metric space; non-linear integral equations
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Jain, D.; Padcharoen, A.; Kumam, P.; Gopal, D. A New Approach to Study Fixed Point of Multivalued Mappings in Modular Metric Spaces and Applications. Mathematics 2016, 4, 51.

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