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Cubic Semi 2-metric Space and Generalized Quasi-pseudo-metric on L-M -semigroup

Associate Professor, Department of Mathematics, Manakula Vinayagar Institute of Technology, Kalitheerthal Kuppam, Puducherry 605 107, India.

Assistant Professor, Department of Mathematics, Measi Academy of Architecture, Royapettah, Chennai 600014, Tamil Nadu, India.

Assistant Professor (Senior Grade), Department of Mathematics (S & H), University College of Engineering, Panruti, (a Constituent College of Anna University Chennai), Panruti 607 106, Tamil Nadu, India.

* Corresponding Author

Annals of Communications in Mathematics 2024

, 8 (1),

57-70.

https://doi.org/10.62072/acm.2025.080105

Received: 10 Jan 2025 |

Accepted: 10 Mar 2025 |

Published: 31 Mar 2025

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Abstract

This paper introduces the novel concepts of semi 2-metric space and interval- valued semi 2-metric space. We establish the fundamental properties of these structures and examine their relationships with existing metric space generalizations. Additionally, it proposes the concept of cubic semi 2-metric spaces by integrating the principles of cubic sets with semi 2-metric spaces. Furthermore, the paper examines the structure of general- ized quasi-pseudometric spaces on L-M -semigroup and investigates the characteristics of the quasi-pseudometric space associated with L-M -semigroup.

Keywords

Cubic semi 2-metric space; Cubic set; fuzzy 2-metric space; Fuzzy semi 2-metric space; Interval-valued fuzzy metric space; M-semigroup; Quasi-metric space; Quasi-pseudo-metric space

Cite This Article

Cubic Semi 2-metric Space and Generalized Quasi-pseudo-metric on L-M -semigroup.

Annals of Communications in Mathematics,

2025,

8 (1):

57-70.

https://doi.org/10.62072/acm.2025.080105

Copyright © 2024 by the Author(s). Licensee Techno Sky Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).