Open Access
2016 Answers to Kirk-Shahzad's Questions on Strong $b$-metric Spaces
Tran Van An, Nguyen Van Dung
Taiwanese J. Math. 20(5): 1175-1184 (2016). DOI: 10.11650/tjm.20.2016.6359

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.

Citation

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Tran Van An. Nguyen Van Dung. "Answers to Kirk-Shahzad's Questions on Strong $b$-metric Spaces." Taiwanese J. Math. 20 (5) 1175 - 1184, 2016. https://doi.org/10.11650/tjm.20.2016.6359

Information

Published: 2016
First available in Project Euclid: 1 July 2017

zbMATH: 1357.54039
MathSciNet: MR3555895
Digital Object Identifier: 10.11650/tjm.20.2016.6359

Subjects:
Primary: 47H10 , 54H25
Secondary: 54D99 , 54E99

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

Rights: Copyright © 2016 The Mathematical Society of the Republic of China

Vol.20 • No. 5 • 2016
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