In this paper, we begin with some observations on F-contractions. Thereafter, we introduce the notion of $(F,\mathcal{R})_{g}$ -contractions and utilize the same to prove some coincidence and common fixed point results in the setting of metric spaces endowed with binary relations. An example is also given to exhibit the utility of our results. We also deduce some consequences in the setting of ordered metric spaces. As an application, we investigate the existence and uniqueness of a solution of integral equation of Volterra type.

中文翻译：

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\（（F，\ mathcal {R}）_ {g} \）- contracts下的关系理论重合和公共不动点结果与一个应用程序

在本文中，我们将从对F收缩的一些观察开始。此后，我们引入$（F，\ mathcal {R}）_ {g} $-收缩的概念，并利用它来证明具有二元关系的度量空间设置中的某些巧合和共同的不动点结果。还给出了一个例子来展示我们的结果的效用。我们还推断出有序度量空间设置中的一些后果。作为一种应用，我们研究了Volterra型积分方程解的存在性和唯一性。