论文标题
最佳接近点会导致拓扑空间和延伸Banach收缩原则
Best proximity point results in topological spaces and extension of Banach contraction principle
论文作者
论文摘要
在本文中，我们介绍了在任意拓扑空间X上定义的拓扑上BANACH收缩映射的概念，借助连续函数$ g：x \ times x \ rightarrow \ mathbb {r} $，并研究了此类映射的固定点。此外，我们介绍了在X的非空子集上定义的两种类型的映射，并产生足够的条件，以确保这些映射的最佳接近点存在。我们的最佳接近点结果还将现有结果从公制空间或Banach空间扩展到拓扑空间。更确切地说，我们新引入的映射比Bunlue和Suantai [Arch]引入的相应概念更笼统。数学。 （BRNO），54（2018），165-176]。我们提出了几个示例，以验证我们的结果并证明其动机是合理的。为了研究最佳接近点结果，我们介绍了X的G链，G序列紧凑的子集的概念，并产生示例，以表明存在X的非空子集，该子集未封闭，在常规拓扑下依次紧凑，但是G链接和G-序列紧凑的。
In this paper, we introduce the notion of topologically Banach contraction mapping defined on an arbitrary topological space X with the help of a continuous function $g:X\times X\rightarrow \mathbb{R}$ and investigate the existence of fixed points of such mapping. Moreover, we introduce two types of mappings defined on a non-empty subset of X and produce sufficient conditions which will ensure the existence of best proximity points for these mappings. Our best proximity point results also extend some existing results from metric spaces or Banach spaces to topological spaces. More precisely, our newly introduced mappings are more general than that of the corresponding notions introduced by Bunlue and Suantai [Arch. Math. (Brno), 54(2018), 165-176]. We present several examples to validate our results and justify its motivation. To study best proximity point results, we introduce the notions of g-closed, g-sequentially compact subsets of X and produce examples to show that there exists a non-empty subset of X which is not closed, sequentially compact under usual topology but is g-closed and g-sequentially compact.
