Abstract

The essential importance of the best proximity point theory is that “best proximity point theory” appears in the coincidence of “metric fixed point theory” and “optimization theory.” So finding best proximity points of mappings satisfying different type of contractive conditions in different structures is one of the fascinating research topics. For this, in this article, we first introduce a new type of proximal property of a pair of subsets of a metric space, which we designate as proximal weakly compact pair. After this, we come up with some new type of proximal contractive and proximal cyclic contractive mappings. Then we investigate the existence of best proximity point(s) in these newly originated mappings in the setting of proximal weakly compact pair of subsets in a metric space.

摘要

最佳邻近点理论的本质重要性在于，“最佳邻近点理论”出现在“度量不动点理论”和“优化理论”的重合中。因此，寻找满足不同结构中不同类型收缩条件的映射的最佳邻近点是引人入胜的研究课题之一。为此，在本文中，我们首先介绍了度量空间的一对子集的一种新型近端性质，我们将其称为近端弱紧对。在此之后，我们提出了一些新型的近端收缩映射和近端循环收缩映射。然后，我们在度量空间中近端弱紧致子集对的设置中研究这些新产生的映射中最佳邻近点的存在。