In this article, we carry out some observations on existing metrical coincidence theorems of Karapinar et al. (Fixed Point Theory Appl. 2014:92, 2014) and Erhan et al. (J. Inequal. Appl. 2015:52, 2015) proved for Lakshmikantham–Ćirić-type nonlinear contractions involving $(f,g)$ -closed transitive sets after proving some coincidence theorems satisfying Boyd–Wong-type nonlinear contractivity conditions employing the idea of $(f,g)$ -closed locally f-transitive binary relation.

中文翻译：

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Boyd-Wong型非线性收缩下关系理论重合定理的观测

在本文中，我们对Karapinar等人的现有度量重合定理进行了一些观察。（Fixed Point Theory Appl.2014：92，2014）和Erhan等人。（J. Inequal。Appl。2015：52，2015）证明了满足$（f，g）$-闭合传递集的Lakshmikantham–Ćirić型非线性收缩，并证明了一些符合定理，并满足Boyd–Wong型非线性收缩条件$（f，g）$的想法-封闭局部f-传递二进制关系。