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A comparative analysis of hypergroupoids derived from metric spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 23 مرداد 1404 اصل مقاله (388.67 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.33780.5038 | ||
| نویسندگان | ||
| Kazem Hamidizadeh1؛ Saeed Mirvakili* 2؛ Rauofeh Manaviyat1؛ Hossein Naraghi1 | ||
| 1Department of Mathematics, Payame Noor University, Tehran, Iran | ||
| 2Department of Mathematical Sciences, Yazd University, Yazd, Iran | ||
| تاریخ دریافت: 25 فروردین 1403، تاریخ بازنگری: 18 تیر 1403، تاریخ پذیرش: 26 تیر 1403 | ||
| چکیده | ||
| This study investigates the correlation between various hypergroupoids and a specified metric space, examining the distinctive characteristics of this hyperstructure. Through rigorous analysis, our inquiry establishes the potential of these hypergroupoids to function as commutative quasihypergroups. Additionally, we delineate specific conditions under which these hypergroupoids exhibit hypergroup properties, shedding light on the complex interplay of these mathematical structures within the context of the given metric space. Finally, a metric space obtained from a given hypergroupoid is introduced. | ||
| کلیدواژه‌ها | ||
| Metric space؛ hypergroupoid؛ Hypergroup؛ $H_v$-group | ||
| مراجع | ||
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[1] S. Banach, Theorie des Operations Lineaires, Monografje Matematyczne, TOM I, 1932. [2] C. Berge, Graphs et Hypergraphs, Dunod, Paris, 1970. [3] C. Berge, Hypergraphs, Elsevier Science Publishers B.V., 1989. [4] P. Corsini and V. Leoreanu, Applications of Hyperstructures Theory, Advances in Mathematics, Kluwer Academic Publishers, 2003. [5] P. Corsini, Prolegomena of Hypergroup Theory, Aviani editor, Second edition, 1993. [6] P. Corsini, Hypergraphs and hypergroups, Algebra Univer. 35 (1996), 548–555. [7] B. Davvaz and T. Vougiouklis, A Walk Through Weak Hyperstructures: Hv-Structure, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2019. [8] B. Davvaz and V. Leoreanu-Fotea, Hyperring Theory and Applications, International Academic Press, USA, 2007. [9] B. Davvaz, Polygroup theory and related systems, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2013. [10] M. Farshi, B. Davvaz, and S. Mirvakili, Degree hypergroupoids associated with hypergraphs, Filomat 28 (2014), 119–129. [11] M. Farshi, B. Davvaz, and S. Mirvakili, Hypergraphs and hypergroups based on a special relation, Commun. Algebra 42 (2014), 3395–3406. [12] I.M. Gelfand, Normierte ringe, Rec. Math. (Mat. Sbornik) 51 (1941), 3–24. [13] F. Marty, Sur une generalization de la notion de group, 8th Cong. Math. Scand., 1934, pp. 45–49. [14] S. Mirvakili and R. Manaviyat, r-hypergroupoids associated with metric spaces, 3rd Seminar Harmonic Anal. Appl., University of Yazd, Iran, 2015, pp. 46. [15] F. Hausdorff, Punktmengen in allgemeinen raumen, grundzage der mengenlehre, Goschens Lehrbucherei/Gruppe I, Reine und Angewandte Mathematik Series, Leipzig: Von Veit, 2011, pp. 211. [In German] [16] J. Von Neumann, Einige satze uber messbare abbildungen, Ann. Math. 33 (1932), no. 3, 574–586. [17] W. Rudin, Principles of Mathematical Analysis, McGraw-Hill, New York, 1976. [18] M.A. Zarei and S. Mirvakili, Hypergroupoids associated with a metric space, 52nd Ann. Iran. Math. Conf., Shahid Bahonar University of Kerman, Iran, 2021, pp. 673–676. | ||
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