Some new results on $\star$-metric spaces

Abhishikta Das; Tarapada Bag

doi:10.54187/jnrs.1367114

EN

Some new results on $\star$-metric spaces

Abstract

The concept of $\star$-metric, based on the relaxation of triangle inequality of metric axioms by using a t-definer, was introduced by Khatami and Mirzavaziri. This paper extends and generalizes some well-known results of classical metric space. Considering the definition of $\star$-metric space, it studies the notion of a closed ball. The paper proves some results related to closed sets, convergent sequences, Cauchy sequences, and the diameter of a set. This paper contains the study on the metrizability of $\star$-metric space and provides an alternative approach to the proof of metrizability for $\star$-metric space using the famous `Niemytski and Wilson's metrization theorem'.

Keywords

t-definer, $\star$-metric space, closed set, metrizability

References

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Details

Primary Language

English

Subjects

Operator Algebras and Functional Analysis

Journal Section

Research Article

Authors

Abhishikta Das
0000-0002-2860-424X
India

Tarapada Bag ^*
0000-0002-8834-7097
India

Publication Date

December 31, 2023

Submission Date

September 27, 2023

Acceptance Date

November 25, 2023

Published in Issue

Year 2023 Volume: 12 Number: 3

DOI

https://doi.org/10.54187/jnrs.1367114

IZ

https://izlik.org/JA45ML56BY

APA

Das, A., & Bag, T. (2023). Some new results on $\star$-metric spaces. Journal of New Results in Science, 12(3), 157-165. https://doi.org/10.54187/jnrs.1367114

AMA

1.Das A, Bag T. Some new results on $\star$-metric spaces. JNRS. 2023;12(3):157-165. doi:10.54187/jnrs.1367114

Chicago

Das, Abhishikta, and Tarapada Bag. 2023. “Some New Results on $\star$-Metric Spaces”. Journal of New Results in Science 12 (3): 157-65. https://doi.org/10.54187/jnrs.1367114.

EndNote

Das A, Bag T (December 1, 2023) Some new results on $\star$-metric spaces. Journal of New Results in Science 12 3 157–165.

IEEE

[1]A. Das and T. Bag, “Some new results on $\star$-metric spaces”, JNRS, vol. 12, no. 3, pp. 157–165, Dec. 2023, doi: 10.54187/jnrs.1367114.

ISNAD

Das, Abhishikta - Bag, Tarapada. “Some New Results on $\star$-Metric Spaces”. Journal of New Results in Science 12/3 (December 1, 2023): 157-165. https://doi.org/10.54187/jnrs.1367114.

JAMA

1.Das A, Bag T. Some new results on $\star$-metric spaces. JNRS. 2023;12:157–165.

MLA

Das, Abhishikta, and Tarapada Bag. “Some New Results on $\star$-Metric Spaces”. Journal of New Results in Science, vol. 12, no. 3, Dec. 2023, pp. 157-65, doi:10.54187/jnrs.1367114.

Vancouver

1.Abhishikta Das, Tarapada Bag. Some new results on $\star$-metric spaces. JNRS. 2023 Dec. 1;12(3):157-65. doi:10.54187/jnrs.1367114