Arbitrary binary relations, contraction mappings and $b$-metric spaces

Keywords: Binary Relations, Contraction Mappings

Abstract

UDC 517.9
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 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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Published
28.03.2020
How to Cite
ChandokS. “Arbitrary Binary Relations, Contraction Mappings and $b$-Metric Spaces”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 4, Mar. 2020, pp. 565-74, doi:10.37863/umzh.v72i4.368.
Section
Research articles