Abstract

In the present paper, we study the existence of best proximity pair in ultrametric spaces. We show, under suitable assumptions, that the proximinal pair \((A,B)\) has a best proximity pair. As a consequence we generalize a well known best approximation result and we derive some fixed point theorems. Moreover, we provide examples to illustrate the obtained results.

中文翻译：

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超测量空间中的最佳邻近对

摘要

在本文中，我们研究了超度量空间中最佳邻近对的存在。我们表明，在适当的假设下，邻近对\((A,B)\)具有最佳邻近对。因此，我们概括了众所周知的最佳近似结果，并推导出了一些不动点定理。此外，我们提供了示例来说明所获得的结果。