Arbitrary binary relations, contraction mappings and $b$-metric spaces
UDC 517.9We prove some results on the existence and uniqueness of fixed points defined on a $b$-metric space endowed with an arbitrary binary relation.  As applications, we obtain some statements on coincidence points involving a pair of mappings.  Our results generalize, e...
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| Date: | 2020 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2020
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/368 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.9We prove some results on the existence and uniqueness of fixed points defined on a $b$-metric space endowed with an arbitrary binary relation.  As applications, we obtain some statements on coincidence points involving a pair of mappings.  Our results generalize, extend, modify and unify several well-known results especially those obtained by Alam and Imdad [J. Fixed Point Theory and Appl., 17, 693–702 (2015); Fixed Point Theory, 18, 415–432 (2017); Filomat, 31, 4421–4439 (2017)] and Berzig [J. Fixed Point Theory and Appl., 12, 221–238 (2012)].  Also, we provide an example to illustrate the suitability of results obtained. |
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| DOI: | 10.37863/umzh.v72i4.368 |