2020 **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…

Help me understand this report

Search citation statements

Paper Sections

Select...

3

1

Citation Types

0

5

0

Year Published

2021

2023

Publication Types

Select...

2

Relationship

2

0

Authors

Journals

(42 citation statements)

(42 reference statements)

0

5

0

“…The study of the characterization of the completeness of a metric space can be traced to Subrahmanyam [29] in 1975, who proved that Kannan's contraction characterizes the metric completeness; that is, a metric space (X, d) is complete if and only if every Kannan's contraction on X has a fixed point. For more on the Completeness Problem in various contexts, we refer the readers to [30,31] and the references therein. The "Completeness Problem" is equivalent to another problem in Behavioral Sciences known as the "End Problem" (see [32]).…”

confidence: 99%

“…The study of the characterization of the completeness of a metric space can be traced to Subrahmanyam [29] in 1975, who proved that Kannan's contraction characterizes the metric completeness; that is, a metric space (X, d) is complete if and only if every Kannan's contraction on X has a fixed point. For more on the Completeness Problem in various contexts, we refer the readers to [30,31] and the references therein. The "Completeness Problem" is equivalent to another problem in Behavioral Sciences known as the "End Problem" (see [32]).…”

confidence: 99%

“…Ciric et al [18] obtained Suzuki type fixed point theorems for generalized multivalued mappings on a set endowed with two b−metrics. Alo et al [19] and Ali et al [20] obtained the existence of fixed points of multivalued quasi-contractions along with a completeness characterization of underlying b−metric spaces.…”

confidence: 99%

“…For details on the completeness problem and the end problem, we refer to [33,34] and references therein. In 1959, Connel presented an example ( [35], (Example 3)) (also compare [20]) which shows that BCP does not characterize metric (b−metric) completeness. That is, there exists an incomplete metric (b−metric) space W such that every Banach contraction on W has a fixed point.…”

confidence: 99%