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 the coincidence of points involving a pair of mappings. Our results generalize, extend, modify and unify several well-known results and, especially, the results obtained by Alam and Imdad [J. Fixed Point Theory Appl., 17, 693–702 (2015); Fixed Point Theory, 18, 415–432 (2017), and Filomat, 31, 4421–4439 (2017)] and Berzig [J. Fixed Point Theory Appl., 12, 221–238 (2012)]. In addition, we provide an example to illustrate the suitability of the obtained results.

中文翻译：

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任意二元关系、收缩映射和 b 度量空间

我们证明了在具有任意二元关系的 b 度量空间上定义的不动点的存在性和唯一性的一些结果。作为应用，我们获得了一些关于涉及一对映射的点的重合的陈述。我们的结果概括、扩展、修改和统一了几个众所周知的结果，特别是 Alam 和 Imdad 获得的结果 [J. 不动点理论应用，17, 693–702 (2015)；不动点理论, 18, 415–432 (2017), and Filomat, 31, 4421–4439 (2017)] 和 Berzig [J. 不动点理论应用，12, 221–238 (2012)]。此外，我们提供了一个例子来说明所获得结果的适用性。