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Galoitica: Journal of Mathematical Structures and Applications

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Galoitica: Journal of Mathematical Structures and Applications
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Volume 10 • Issue 2 • PP: 08-18 • 2024

On Soft 2-metric spaces

Pshtiwan Sabir Noori 1*
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1Sherko Bekas High School, Kirkuk General Education Directorate, Kirkuk, Iraq
* Corresponding Author.
DOI https://doi.org/10.54216/GJMSA.0100201
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© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Received: October 10, 2023 Revised: January 11, 2024 Accepted: March 10, 2024
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Abstract

The main purpose of this article is to introduce the concept of soft2-metric spaces that are new metric spaces based on the soft-elements and to study their properties, also to introduce some related concepts such as soft2- open ball, soft2 closed ball, soft2- open sets, soft2 closed sets, soft2-interior elements, soft2-limit elements, soft2-closure of sets, and study some of their properties.  And that is proved that every soft2- open ball is a soft2- open set, every soft2- closed ball is a soft2- closed set.  And reformulated and proved some theorems in soft2-metric space, such as Cantor's theorem and other theorems.

Keywords

soft2-elements soft2-metric spaces soft2- open sets soft2-closed sets.

References

[1]     S. Gähler, “2-metrische Räume und ihre topologische Struktur”. Math. Nachr. 26, 115-118 (1963).

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[3]     S. Gahler, “Über die uniformisierbarkeit 2-metrischer Räume”, Math. Nachr., 28 (1965), 235-244.

[4]     K. Iseki, “Fixed point theorems in 2-metric spaces”, Math. Seminar Notes, Kobe Univ., 3 (1975), 133-136.

[5]     B. K. Lahiri, P. Das and L. K. Dey, “Cantor’s theorem in 2-metric spaces and its applications to fixed point problems”. Taiwanese J Math 15:337–352 (2011).

[6]     D. Molodtsov, “Soft Set Theory First Results” Computers and Mathematics with Applications 37 (1999) 19-31.

[7]     S. Das and S. K. Samanta. “Soft Real Sets, Soft Real Numbers and Their Properties”. The Journal of Fuzzy Mathematics Vol. 20 No. 3, 2012.

[8]     P. K. Maji, R. Biswas, and A. R. Roy. “Soft Set Theory “Computers and Mathematics with  Applications 45 (2003) 555-562.

[9]     P. Majumdar, S. K. Samanta “Similarity measure of soft sets” New Mathematics and Natural Computation ·Vol. 4, No. 1 (2008).

[10]   D. Pei, D. Miao. “From Soft Sets to Information Systems” Granular Computing, 2005, IEEE International Conference, Volume - 2. 617 – 622.

[11]   P. Zhu and Q. Wen, “Operation of Soft Sets Revisited” Hindawi Publishing Corporation Journal Applied Mathematics. (2013).

[12]   A. Sezgin and A. O. Atagun, “On operations of soft sets,” Computers & Mathematics with    Applications, vol. 61, no. 5, pp. 1457–1467, (2011).

[13]   S. Das and S. K. Samanta, “One soft metric space”. The Journal of Fuzzy Mathematics. Vol. 21, No. 3 (2013).

 

 

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Noori, Pshtiwan Sabir. "On Soft 2-metric spaces." Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 10, no. Issue 2, 2024, pp. 08-18. DOI: https://doi.org/10.54216/GJMSA.0100201
Noori, P. (2024). On Soft 2-metric spaces. Galoitica: Journal of Mathematical Structures and Applications, Volume 10(Issue 2), 08-18. DOI: https://doi.org/10.54216/GJMSA.0100201
Noori, Pshtiwan Sabir. "On Soft 2-metric spaces." Galoitica: Journal of Mathematical Structures and Applications Volume 10, no. Issue 2 (2024): 08-18. DOI: https://doi.org/10.54216/GJMSA.0100201
Noori, P. (2024) 'On Soft 2-metric spaces', Galoitica: Journal of Mathematical Structures and Applications, Volume 10(Issue 2), pp. 08-18. DOI: https://doi.org/10.54216/GJMSA.0100201
Noori P. On Soft 2-metric spaces. Galoitica: Journal of Mathematical Structures and Applications. 2024;Volume 10(Issue 2):08-18. DOI: https://doi.org/10.54216/GJMSA.0100201
P. Noori, "On Soft 2-metric spaces," Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 10, no. Issue 2, pp. 08-18, 2024. DOI: https://doi.org/10.54216/GJMSA.0100201
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