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

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

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 c...

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Bibliographic Details
Main Authors: Dilip Jain, Anantachai Padcharoen, Poom Kumam, Dhananjay Gopal
Format: Article
Language:English
Published: MDPI AG 2016-08-01
Series:Mathematics
Subjects:
Keywords
fixed point
multivalued F-contractive
modular metric space
non-linear integral equations
Online Access:http://www.mdpi.com/2227-7390/4/3/51
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spelling doaj-81879bc13e0343e5a8d446fb02df43ad2020-11-25T00:16:57ZengMDPI AGMathematics2227-73902016-08-01435110.3390/math4030051math4030051A New Approach to Study Fixed Point of Multivalued Mappings in Modular Metric Spaces and ApplicationsDilip Jain0Anantachai Padcharoen1Poom Kumam2Dhananjay Gopal3Department of Applied Mathematics & Humanities, S.V. National Institute of Technology, Surat-395007 Gujarat, IndiaDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, ThailandDepartment of Applied Mathematics & Humanities, S.V. National Institute of Technology, Surat-395007 Gujarat, IndiaThe 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.http://www.mdpi.com/2227-7390/4/3/51Keywordsfixed pointmultivalued F-contractivemodular metric spacenon-linear integral equations
collection DOAJ
language English
format Article
sources DOAJ
author Dilip Jain
Anantachai Padcharoen
Poom Kumam
Dhananjay Gopal
spellingShingle Dilip Jain
Anantachai Padcharoen
Poom Kumam
Dhananjay Gopal
A New Approach to Study Fixed Point of Multivalued Mappings in Modular Metric Spaces and Applications
Mathematics
Keywords
fixed point
multivalued F-contractive
modular metric space
non-linear integral equations
author_facet Dilip Jain
Anantachai Padcharoen
Poom Kumam
Dhananjay Gopal
author_sort Dilip Jain
title A New Approach to Study Fixed Point of Multivalued Mappings in Modular Metric Spaces and Applications
title_short A New Approach to Study Fixed Point of Multivalued Mappings in Modular Metric Spaces and Applications
title_full A New Approach to Study Fixed Point of Multivalued Mappings in Modular Metric Spaces and Applications
title_fullStr A New Approach to Study Fixed Point of Multivalued Mappings in Modular Metric Spaces and Applications
title_full_unstemmed A New Approach to Study Fixed Point of Multivalued Mappings in Modular Metric Spaces and Applications
title_sort new approach to study fixed point of multivalued mappings in modular metric spaces and applications
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2016-08-01
description 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.
topic Keywords
fixed point
multivalued F-contractive
modular metric space
non-linear integral equations
url http://www.mdpi.com/2227-7390/4/3/51
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