@article{Chandok_2020, title={Arbitrary binary relations, contraction mappings and $b$-metric spaces}, volume={72}, url={http://umj.imath.kiev.ua/index.php/umj/article/view/368}, DOI={10.37863/umzh.v72i4.368}, abstractNote={<p>UDC 517.9<br>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., <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.</p>}, number={4}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Chandok, S.}, year={2020}, month={Mar.}, pages={565-574} }