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