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Extended Proinov X -contractions in metric spaces and fuzzy metric spaces satisfying the property NC by avoiding the monotone condition

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dc.contributor.author Karapınar, Erdal
dc.contributor.author Martínez-Moreno, Juan
dc.contributor.author Shahzad, Naseer
dc.contributor.author Roldán López de Hierro, Antonio Francisco
dc.date.accessioned 2024-03-21T12:52:50Z
dc.date.available 2024-03-21T12:52:50Z
dc.date.issued 2022-10
dc.identifier.citation Karapınar, Erdal;...et.al. (2022). "Extended Proinov X -contractions in metric spaces and fuzzy metric spaces satisfying the property NC by avoiding the monotone condition", Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, Vol.116, No.4, pp.1-28. tr_TR
dc.identifier.issn 15787303
dc.identifier.uri http://hdl.handle.net/20.500.12416/7685
dc.description.abstract In recent years, Fixed Point Theory has achieved great importance within Nonlinear Analysis especially due to its interesting applications in real-world contexts. Its methodology is based on the comparison between the distances between two points and their respective images through a nonlinear operator. This comparison is made through contractive conditions involving auxiliary functions whose role is increasingly decisive, and which are acquiring a prominent role in Functional Analysis. Very recently, Proinov introduced new fixed point results that have very much attracted the researchers’ attention especially due to the extraordinarily weak conditions on the auxiliary functions considered. However, one of them, the nondecreasing character of the main function, has been used for many years without the chance of being replaced by another alternative property. In this way, several researchers have recently raised this question as an open problem in this field of study. In order to face this open problem, in this work we introduce a novel class of auxiliary functions that serve to define contractions, both in metric spaces and in fuzzy metric spaces, which, in addition to generalizing to Proinov contractions, avoid the nondecreasing character of the main auxiliary function. Furthermore, we present these new results in the setting of fuzzy metric spaces that satisfy the condition NC, which open new possibilities in the metric theory compared to classic non-Archimedean fuzzy metric spaces. Finally, we include some illustrative examples to show how to apply the novel theorems to cases that are not covered by other previous results. tr_TR
dc.language.iso eng tr_TR
dc.relation.isversionof 10.1007/s13398-022-01268-8 tr_TR
dc.rights info:eu-repo/semantics/openAccess tr_TR
dc.subject Contractivity Condition tr_TR
dc.subject Fixed Point tr_TR
dc.subject Fuzzy Metric Space tr_TR
dc.subject Proinov Theorem tr_TR
dc.subject Property NC tr_TR
dc.title Extended Proinov X -contractions in metric spaces and fuzzy metric spaces satisfying the property NC by avoiding the monotone condition tr_TR
dc.type article tr_TR
dc.relation.journal Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas tr_TR
dc.contributor.authorID 19184 tr_TR
dc.identifier.volume 116 tr_TR
dc.identifier.issue 4 tr_TR
dc.identifier.startpage 1 tr_TR
dc.identifier.endpage 28 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü tr_TR


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