Arbitrary binary relations, contraction mappings and b -metric spaces

Abstract

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., <strong>17</strong>, 693–702 (2015); Fixed Point Theory, <strong>18</strong>, 415–432 (2017); Filomat, <strong>31</strong>, 4421–4439 (2017)] and Berzig [J. Fixed Point Theory and Appl., <strong>12</strong>, 221–238 (2012)]. Also, we provide an example to illustrate the suitability of results obtained.