In this paper, we introduce a new concept of dominating proximal generalized Geraghty for two mappings and prove the existence and uniqueness of a common best proximity coincidence point in complete metric spaces. And also, we give an example for the main theorems. The main theorem is a generalization and improvement of some well-known theorems.

中文翻译：

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完备度量空间中支配近邻广义象限的通用最佳邻近点重合点定理

在本文中，我们为两个映射引入了一种控制近邻广义Geraghty的新概念，并证明了在完整度量空间中一个公共的最佳邻近重合点的存在和唯一性。并且，我们给出一个主要定理的例子。主要定理是对一些著名定理的推广和改进。