2020/07/21 by Sumit Som, Som, Sumit, Supriti Laha +3
Computer Science · Mathematics · #FOS: Mathematics #Fixed Point Theorems Analysis #General Topology (math.GN) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2007.10852
openalex publication_date 2020/07/21 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In this paper, we introduce the notion of topologically Banach contraction\nmapping defined on an arbitrary topological space X with the help of a\ncontinuous function g:X\× X\→ \ℝ and investigate the\nexistence of fixed points of such mapping. Moreover, we introduce two types of\nmappings defined on a non-empty subset of X and produce sufficient conditions\nwhich will ensure the existence of best proximity points for these mappings.\nOur best proximity point results also extend some existing results from metric\nspaces or Banach spaces to topological spaces. More precisely, our newly\nintroduced mappings are more general than that of the corresponding notions\nintroduced by Bunlue and Suantai [Arch. Math. (Brno), 54(2018), 165-176]. We\npresent several examples to validate our results and justify its motivation. To\nstudy best proximity point results, we introduce the notions of g-closed,\ng-sequentially compact subsets of X and produce examples to show that there\nexists a non-empty subset of X which is not closed, sequentially compact under\nusual topology but is g-closed and g-sequentially compact.\n