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dc.contributor.authorKarapinar, Erdal
dc.contributor.authorRoldán López de Hierro, Antonio Francisco
dc.identifier.citationKarapınar, E... [et al.]. Extended Proinov X-contractions in metric spaces and fuzzy metric spaces satisfying the property NC by avoiding the monotone condition. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 116, 140 (2022). []es_ES
dc.description.abstractIn 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 themain auxiliary function. Furthermore, we present these new results in the setting of fuzzy metric spaces that satisfy the conditionNC, 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.es_ES
dc.description.sponsorshipUniversidad de Granada / CBUAes_ES
dc.rightsAtribución 4.0 Internacional*
dc.subjectFixed pointes_ES
dc.subjectFuzzy metric spacees_ES
dc.subjectContractivity conditiones_ES
dc.subjectProperty NCes_ES
dc.subjectProinov theoremes_ES
dc.titleExtended Proinov X-contractions in metric spaces and fuzzy metric spaces satisfying the property NC by avoiding the monotone conditiones_ES

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Atribución 4.0 Internacional
Except where otherwise noted, this item's license is described as Atribución 4.0 Internacional