Completeness of b∼Metric Spaces and the Fixed Points of Generalized Multivalued Quasicontractions

Abstract EN

In this article, we present a completeness characterization of b∼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∼ metric spaces and (b) to establish completeness of a b∼ 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.