Completeness of \(b\sim\) metric spaces and the fixed points of generalized multivalued quasicontractions (Q2004182)

Summary: In this article, we present a completeness characterization of \(b\sim\) metric space via existence of fixed points of generalized multivalued quasicontractions. The purpose of this paper is twofold: (a) to establish the existence of fixed points of multivalued quasicontractions in the setup of \(b\sim\) metric spaces and (b) to establish completeness of a \(b\sim\) metric space which is a topological property in nature with existence of fixed points of generalized multivalued quasicontractions. Further, a comparison of our results with comparable results shows that the results obtained herein improve and unify the existing results in the literature applicable to the case where existing results fail.