Open AccessArbitrary binary relations, contraction mappings and b -metric spaces
Author(s) -
Sumit Chandok
Publication year - 2020
Publication title -
ukraïnsʹkij matematičnij žurnal
Language(s) - English
Resource type - Journals
ISSN - 1027-3190
DOI - 10.37863/umzh.v72i4.368
Subject(s) - uniqueness , metric space , binary number , mathematics , fixed point , binary relation , fixed point theorem , algorithm , discrete mathematics , combinatorics , mathematical analysis , arithmetic
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.