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A fixed point principle in ordered metric spaces and applications to rational type contractions

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dc.contributor.author Eroglu, I.
dc.contributor.author Guner, E.
dc.contributor.author Aygun, H.
dc.contributor.author Valero, O.
dc.date.accessioned 2024-03-26T06:39:27Z
dc.date.available 2024-03-26T06:39:27Z
dc.date.issued 2022
dc.identifier.citation Eroglu, I., Guner, E., Aygun, H., Valero, O. (2022). A fixed point principle in ordered metric spaces and applications to rational type contractions. AIMS Math., 7(7), 13573-13594. https://doi.org/10.3934/math.2022750 en_US
dc.identifier.issn 2473-6988
dc.identifier.uri http://dx.doi.org/10.3934/math.2022750
dc.identifier.uri https://www.webofscience.com/wos/woscc/full-record/WOS:000824214100001
dc.identifier.uri http://earsiv.odu.edu.tr:8080/xmlui/handle/11489/5137
dc.description WoS Categories: Mathematics, Applied; Mathematics en_US
dc.description Web of Science Index: Science Citation Index Expanded (SCI-EXPANDED) en_US
dc.description Research Areas: Mathematics en_US
dc.description.abstract Fixed points results for rational type contractions in metric spaces have been widely studied in the literature. In the last years, many of these results are obtained in the context of partially ordered metric spaces. In this paper, we introduce a fixed point principle for a class of mappings between partially ordered metric spaces that we call orbitally order continuous. We show that the hypotheses in the statement of such a principle are not redundant and, in addition, that they cannot be weakened in order to guarantee the existence of a fixed point. Moreover, the relationship between this kind of mappings and those that are continuous and orbitally continuous is discussed. As an application, we extend many fixed point theorems for continuous contractions of rational type to the framework of those that are only orbitally order continuous. Furthermore, we get extensions of the aforementioned metric fixed point results to the framework of partial metrics. This is achieved thanks to the fact that each partial metric induces in a natural way a metric in such a way that our new principle is applicable. In both approaches, the metric and the partial metric, we show that there are orbitally order continuous mappings that satisfy all assumptions in our new fixed point principle but that they are not contractions of rational type. The explored theory is illustrated by means of appropriate examples. en_US
dc.description.sponsorship European Union?s Horizon 2020 research and innovation programme [PGC2018-095709-B-C21, 871260]; MCIN/AEI/y FEDER Una manera de hacer Europa [PGC2018-095709-B-C21]; project BUGWRIGHT2; European Union's Horizon 2020 research and innovation programme [871260] en_US
dc.language.iso eng en_US
dc.publisher AMER INST MATHEMATICAL SCIENCES-AIMS-SPRINGFIELD en_US
dc.relation.isversionof 10.3934/math.2022750 en_US
dc.rights info:eu-repo/semantics/openAccess en_US
dc.subject partial order, metric space, partial metric space, fixed point principle, rational contraction en_US
dc.subject GENERALIZED CONTRACTIONS, THEOREMS en_US
dc.title A fixed point principle in ordered metric spaces and applications to rational type contractions en_US
dc.type article en_US
dc.relation.journal AIMS MATHEMATICS en_US
dc.contributor.department Ordu Üniversitesi en_US
dc.contributor.authorID 0000-0002-6969-400X en_US
dc.contributor.authorID 0000-0003-3263-3884 en_US
dc.identifier.volume 7 en_US
dc.identifier.issue 7 en_US
dc.identifier.startpage 13573 en_US
dc.identifier.endpage 13594 en_US


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