In this work, we study existence and convergence of best proximity points of a cyclic contraction mapping in a complete \(\mathrm{{CAT}}_\mathrm{{p}}(0)\) metric space, with \(p \ge 2\). The case of coupled best proximity points of a pair of cyclic contraction mappings is also discussed. As an application, we provide sufficient conditions to obtain an extension of the Banach Contraction Principle for coupled fixed points.

中文翻译：

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$$ \ mathrm {{CAT}} _ \ mathrm {{p}}（0）$$ CATp（0）空间中最佳邻近点的存在和收敛

在这项工作中，我们研究了完整\（\ mathrm {{CAT}} _ \ mathrm {{p}}（0）\）度量空间中具有\（p的循环收缩映射的最佳邻近点的存在和收敛性。\ ge 2 \）。还讨论了一对循环收缩映射的耦合最佳邻近点的情况。作为一种应用，我们提供了充分的条件来获得耦合固定点的Banach收缩原理的扩展。