Taiwanese Journal of Mathematics

Answers to Kirk-Shahzad's Questions on Strong $b$-metric Spaces

Tran Van An and Nguyen Van Dung

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Abstract

In this paper, two open questions on strong $b$-metric spaces posed by Kirk and Shahzad [11, Chapter 12] are investigated. A counterexample is constructed to give a negative answer to the first question, and a theorem on the completion of a strong $b$-metric space is proved to give a positive answer to the second question.

Article information

Source
Taiwanese J. Math., Volume 20, Number 5 (2016), 1175-1184.

Dates
First available in Project Euclid: 1 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1498874523

Digital Object Identifier
doi:10.11650/tjm.20.2016.6359

Mathematical Reviews number (MathSciNet)
MR3555895

Zentralblatt MATH identifier
1357.54039

Subjects
Primary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 54H25: Fixed-point and coincidence theorems [See also 47H10, 55M20]
Secondary: 54D99: None of the above, but in this section 54E99: None of the above, but in this section

Keywords
strong $b$-metric $b$-metric completion Nadler's theorem

Citation

An, Tran Van; Dung, Nguyen Van. Answers to Kirk-Shahzad's Questions on Strong $b$-metric Spaces. Taiwanese J. Math. 20 (2016), no. 5, 1175--1184. doi:10.11650/tjm.20.2016.6359. https://projecteuclid.org/euclid.twjm/1498874523


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