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Arbitrary Binary Relations, Contraction Mappings, and b-Metric Spaces

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Ukrainian Mathematical Journal Aims and scope

We 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 the coincidence of points involving a pair of mappings. Our results generalize, extend, modify and unify several well-known results and, especially, the results obtained by Alam and Imdad [J. Fixed Point Theory Appl., 17, 693–702 (2015); Fixed Point Theory, 18, 415–432 (2017), and Filomat, 31, 4421–4439 (2017)] and Berzig [J. Fixed Point Theory Appl., 12, 221–238 (2012)]. In addition, we provide an example to illustrate the suitability of the obtained results.

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Authors and Affiliations

  1. School of Mathematics, Thapar University, Patiala, India

    S. Chandok

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  1. S. Chandok
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Correspondence to S. Chandok.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 4, pp. 565–574, April, 2020.

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Chandok, S. Arbitrary Binary Relations, Contraction Mappings, and b-Metric Spaces. Ukr Math J 72, 651–662 (2020). https://doi.org/10.1007/s11253-020-01806-w

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  • DOI: https://doi.org/10.1007/s11253-020-01806-w

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