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Hyperoperations on metric spaces: A new frontier | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 02 بهمن 1403 اصل مقاله (372.49 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.33567.5008 | ||
| نویسندگان | ||
| Saeed Mirvakili* 1؛ Kazem Hamidizadeh2؛ Rauofeh Manaviyat2؛ Hossein Naraghi2 | ||
| 1Department of Mathematical Sciences, Yazd University, Yazd, Iran | ||
| 2Department of Mathematics, Payame Noor University, Tehran, Iran | ||
| تاریخ دریافت: 27 اسفند 1402، تاریخ بازنگری: 02 تیر 1403، تاریخ پذیرش: 09 تیر 1403 | ||
| چکیده | ||
| This paper introduces novel hyperoperations on metric spaces. While generally non-commutative, these hyperoperations satisfy the weak commutative property. We further establish necessary and sufficient conditions for associativity. Finally, we obtain a class of $\Gamma$-$H_v$-groups. | ||
| کلیدواژهها | ||
| Metric space؛ $H_v$-group؛ Hypergroup؛ Semihypergroup | ||
| مراجع | ||
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[1] S. Banach, Theorie des Operations Lineaires, Monografje Matematyczne, TOM I, 1932. [2] P. Corsini, Prolegomena of Hypergroup Theory, Second Edition, Aviani editor, 1993. [3] P. Corsini, Hypergraphs and hypergroups, Algebra Univer. 35 (1996), 548–555. [4] P. Corsini and V. Leoreanu, Applications of Hyperstructures Theory, Advanced in Mathematics, Kluwer Academic Publisher, 2003. [5] B. Davvaz and T. Vougiouklis, A Walk Through Weak Hyperstructures: Hv-Structure, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2019. [6] I. Gelfand, Normierte ringe, Mat. Sbornik 9 (1941), no. 1, 3–24. [7] K. Hamidizadeh, S. Mirvakili, R. Manaviyat, and H. Naraghi, A comparative analysis of hypergroupoids derived from metric spaces, Int. J. Nonlinear Anal. to appear. [8] F. Hausdorff, Grundzuge der Mengenlehre, Vol. 7, von Veit, 1914. [9] A. Nikkhah, B. Davvaz, and S. Mirvakili, Hypergroups constructed from hypergraphs, Filomat 32 (2018), no. 10, 3487–3494. [10] W. Rudin, Principles of Mathematical Analysis, McGraw-Hill, New York, 1976. [11] J. Von Neumann, Einige satze ubermessbare abbildungen, Ann. Math. 33 (1932), no. 3, 574–586. | ||
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