Abstract

In this paper, hybrid best proximity points for a class of proximally mixed monotone set-valued mappings are discussed. In order to get rid of the fetter of continuity, we introduce the proximally ordered contraction instead of various proximal distance contractions widely applied in recent literatures and present some new existence and iterative approximation theorems of best proximity points for such mappings. Some examples are given to illustrate the advantages of the obtained results.

中文翻译：

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集值映射的混合最佳邻近点的存在性和迭​​代逼近*

摘要

在本文中，讨论了一类近端混合单调集值映射的混合最佳邻近点。为了摆脱连续性的束缚，我们引入了近端有序收缩而不是最近文献中广泛应用的各种近端距离收缩，并提出了这种映射的最佳邻近点的一些新存在和迭代逼近定理。给出了一些例子来说明所得结果的优点。