TY - JOUR
AU - S. Chandok
PY - 2020/03/28
Y2 - 2022/10/07
TI - Arbitrary binary relations, contraction mappings and $b$-metric spaces
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 72
IS - 4
SE - Research articles
DO - 10.37863/umzh.v72i4.368
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/368
AB - 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., 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.
ER -