1
Sherko Bekas High School, Kirkuk General Education Directorate, Kirkuk, Iraq
(pshtiwanmath6@gmail.com)
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).
[2] S. Gahler, “Lineare 2-normierte Räume”, Math. Nachr., 28 (1965), 1-43.
[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).
| Style | # |
|---|---|
| MLA | Pshtiwan Sabir Noori. "On Soft 2-metric spaces." Galoitica: Journal of Mathematical Structures and Applications, Vol. 10, No. 2, 2024 ,PP. 08-18 (Doi : https://doi.org/10.54216/GJMSA.0100201) |
| APA | Pshtiwan Sabir Noori. (2024). On Soft 2-metric spaces. Journal of Galoitica: Journal of Mathematical Structures and Applications, 10 ( 2 ), 08-18 (Doi : https://doi.org/10.54216/GJMSA.0100201) |
| Chicago | Pshtiwan Sabir Noori. "On Soft 2-metric spaces." Journal of Galoitica: Journal of Mathematical Structures and Applications, 10 no. 2 (2024): 08-18 (Doi : https://doi.org/10.54216/GJMSA.0100201) |
| Harvard | Pshtiwan Sabir Noori. (2024). On Soft 2-metric spaces. Journal of Galoitica: Journal of Mathematical Structures and Applications, 10 ( 2 ), 08-18 (Doi : https://doi.org/10.54216/GJMSA.0100201) |
| Vancouver | Pshtiwan Sabir Noori. On Soft 2-metric spaces. Journal of Galoitica: Journal of Mathematical Structures and Applications, (2024); 10 ( 2 ): 08-18 (Doi : https://doi.org/10.54216/GJMSA.0100201) |
| IEEE | Pshtiwan Sabir Noori, On Soft 2-metric spaces, Journal of Galoitica: Journal of Mathematical Structures and Applications, Vol. 10 , No. 2 , (2024) : 08-18 (Doi : https://doi.org/10.54216/GJMSA.0100201) |