  In this article, we introduce the notions of sequentially compactness and
boundedly compactness in the framework of a newly defined $b_v(s)$-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.
