2018/02/09 by Hiranmoy Garai, Lakshmi Kanta Dey, Garai, Hiranmoy +3 · 1 citation
Mathematics · #47H10 #54H25 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:47H10 #msc:54H25
paper · pdf · doi:10.48550/arxiv.1802.03136
15 pages
arxiv created 2018/02/09 · arxiv updated 2018/02/12
In this article, we introduce the notions of sequentially compactness and boundedly compactness in the framework of a newly defined bv(s)-metric space which is a generalization of usual metric spaces and several other abstract spaces. We establish correlations between sequentially compactness and boundedly compactness. Moreover, we prove some fixed point results of contractive mapping in this setting, from which we can deduce several analogous fixed point results. Finally, we illustrate some non-trivial examples to validate the significances and motivations of this manuscript.