New Fixed Point Results for Modified Contractions and Applications

In this study, we introduce a new type of contractive mapping to establish the existence and uniqueness of fixed points for this type of contraction. Some related examples are built demonstrating the superiority of our results compared to the existing onesin the literature. As applications of the re...

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Main Authors: Hüseyİn Işık, Hassen Aydi, Mohd Salmi Md Noorani, Haitham Qawaqneh
Format: Article
Language:English
Published: MDPI AG 2019-05-01
Series:Symmetry
Subjects:
Online Access:https://www.mdpi.com/2073-8994/11/5/660
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author Hüseyİn Işık
Hassen Aydi
Mohd Salmi Md Noorani
Haitham Qawaqneh
author_facet Hüseyİn Işık
Hassen Aydi
Mohd Salmi Md Noorani
Haitham Qawaqneh
author_sort Hüseyİn Işık
collection DOAJ
description In this study, we introduce a new type of contractive mapping to establish the existence and uniqueness of fixed points for this type of contraction. Some related examples are built demonstrating the superiority of our results compared to the existing onesin the literature. As applications of the results obtained, some new fixed point theorems are presented for graph-type contractions. Furthermore, sufficient conditions are discussed to ensure the existence underlying various approaches of a solution for a functional equation originating in dynamic programming.
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spelling doaj.art-07bd79eaa7fb499aa115660d3ca7326c2022-12-22T04:01:03ZengMDPI AGSymmetry2073-89942019-05-0111566010.3390/sym11050660sym11050660New Fixed Point Results for Modified Contractions and ApplicationsHüseyİn Işık0Hassen Aydi1Mohd Salmi Md Noorani2Haitham Qawaqneh3Department of Mathematics, Faculty of Science and Arts, Muş Alparslan University, Muş 49100, TurkeyDepartment of Mathematics, College of Education of Jubail, Imam Abdulrahman Bin Faisal University, P.O. 12020, Industrial Jubail 31961, Saudi ArabiaSchool of mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, MalaysiaSchool of mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, MalaysiaIn this study, we introduce a new type of contractive mapping to establish the existence and uniqueness of fixed points for this type of contraction. Some related examples are built demonstrating the superiority of our results compared to the existing onesin the literature. As applications of the results obtained, some new fixed point theorems are presented for graph-type contractions. Furthermore, sufficient conditions are discussed to ensure the existence underlying various approaches of a solution for a functional equation originating in dynamic programming.https://www.mdpi.com/2073-8994/11/5/660admissible mappingα-ψ-contractiongraphfunctional equation
spellingShingle Hüseyİn Işık
Hassen Aydi
Mohd Salmi Md Noorani
Haitham Qawaqneh
New Fixed Point Results for Modified Contractions and Applications
Symmetry
admissible mapping
α-ψ-contraction
graph
functional equation
title New Fixed Point Results for Modified Contractions and Applications
title_full New Fixed Point Results for Modified Contractions and Applications
title_fullStr New Fixed Point Results for Modified Contractions and Applications
title_full_unstemmed New Fixed Point Results for Modified Contractions and Applications
title_short New Fixed Point Results for Modified Contractions and Applications
title_sort new fixed point results for modified contractions and applications
topic admissible mapping
α-ψ-contraction
graph
functional equation
url https://www.mdpi.com/2073-8994/11/5/660
work_keys_str_mv AT huseyinisık newfixedpointresultsformodifiedcontractionsandapplications
AT hassenaydi newfixedpointresultsformodifiedcontractionsandapplications
AT mohdsalmimdnoorani newfixedpointresultsformodifiedcontractionsandapplications
AT haithamqawaqneh newfixedpointresultsformodifiedcontractionsandapplications