Completeness of \(b\sim\) metric spaces and the fixed points of generalized multivalued quasicontractions
type: Item
instance of: scholarly article
title: Completeness of \(b\sim\) metric spaces and the fixed points of generalized multivalued quasicontractions
zbMATH Open document ID: 1459.54024
DOI: 10.1155/2020/5183291
author: Basit Ali
author: M. Abbas
author: M. De la Sen
published in: Discrete Dynamics in Nature and Society
publication date: 2020-10-14T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 54E50
Mathematics Subject Classification ID: 54E40
zbMATH DE Number: 7260917
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/5183291
OpenAlex ID: W3082237623
cites work: Variational principles, completeness and the existence of traps in behavioral sciences
cites work: Various generalizations of metric spaces and fixed point theorems
cites work: Q4884981
cites work: Round-off stability of iteration procedures for operators in \(b\)-metric spaces
cites work: Q4225413
cites work: Suzuki type fixed point theorems for generalized multi-valued mappings on a set endowed with two \(b\)-metrics
cites work: Some coincidence theorems and stability of iterative procedures
cites work: Stone-type theorem on \(b\)-metric spaces and applications
cites work: Q3622754
cites work: Basic inequality on a \(b\)-metric space and its applications
cites work: A generalized Banach contraction principle that characterizes metric completeness
cites work: Q5610908
cites work: Some Results on Fixed Points--II
cites work: Completeness and fixed-points
cites work: Properties of Fixed Point Spaces
cites work: On a converse to Banach’s Fixed Point Theorem
cites work: A Generalization of Banach's Contraction Principle
cites work: Multi-valued contraction mappings
cites work: Fixed point theory for set-valued quasi-contraction maps in metric spaces
cites work: Three fixed point theorems for generalized contractions with constants in complete metric spaces
cites work: Common fixed point results in metric-type spaces
cites work: On relaxations of contraction constants and Caristi's theorem in \(b\)-metric spaces
cites work: A fixed point theorem for set-valued quasi-contractions in \(b\)-metric spaces
cites work: Some fixed point results for multi-valued mappings in \(b\)-metric spaces
cites work: Characterization of a b-metric space completeness via the existence of a fixed point of Ciric-Suzuki type quasi-contractive multivalued operators and applications
cites work: Some similarity between contractions and Kannan mappings
cites work: Q5663096
cites work: Q3723318
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description: scientific article; zbMATH DE number 7260917