Completeness of b∼Metric Spaces and the Fixed Points of Generalized Multivalued Quasicontractions. (2nd September 2020)

• Record Type: Journal Article
• Authors: Ali, Basit; Abbas, Mujahid; Sen, Manuel de la
• Other Names: Ding Xiaohua Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2020(2020)
• Publication Date: 2020-09-02
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2020/5183291
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : 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.