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Mazur-Ulam theorem in intuitionistic fuzzy normed spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 1، دوره 17، شماره 4، تیر 2026، صفحه 1-10 اصل مقاله (355.26 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.34107.5088 | ||
| نویسندگان | ||
| Alireza Pourmoslemi* 1؛ Kamal Fallahi2؛ Seiedeh Roghaye Fatemi Nezhad1 | ||
| 1Department of Mathematics, Payame Noor University, P.O.BOX 19395-3697, Tehran, Iran | ||
| 2Javanroud Faculty of Management and Accounting, Razi University, Kermanshah, Iran | ||
| تاریخ دریافت: 23 اردیبهشت 1403، تاریخ بازنگری: 15 مرداد 1403، تاریخ پذیرش: 14 شهریور 1403 | ||
| چکیده | ||
| In this paper, introducing the notion of intuitionistic strictly convex sets, and using functions that preserve equality of intuitionistic fuzzy distance, a new generalization of Mazur-Ulam theorem in intuitionistic fuzzy normed spaces is presented. Moreover, intuitionistic fuzzy isometries, segment-preserving functions, and norm-additive maps are used to study the prerequisites needed to prove the main theorem. | ||
| کلیدواژهها | ||
| Mazur-Ulam theorem؛ Intuitionistic fuzzy normed space؛ Intuitionistic strictly convex sets؛ Intuitionistic fuzzy distance | ||
| مراجع | ||
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[1] C. Alaca, D. Turkoglu, and C. Yildiz, Fixed points in intuitionistic fuzzy metric spaces, Chaos Solitons Fractals 29 (2006), no. 5, 1073–1078. [2] K.T. Atanassov, On Intuitionistic Fuzzy Sets Theory, Vol. 283, Springer, 2012. [3] K.T. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Sets Syst. 33 (1989), no. 1, 37–45. [4] K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst. 20 (1986), 87–96. [5] K.T. Atanassov, Intuitionistic fuzzy sets, Studia Math. 45 (1983), no. 1, 43–48. [6] J.A. Baker, Isometries in normed spaces, Amer. Math. Monthly 78 (1971), no. 6, 655–658. [7] D. Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets Syst. 88 (1997), no. 1, 81–89. [8] M. Eshaghi Gordji and N. Ghobadipour, On the Mazur-Ulam theorem in fuzzy normed spaces, arXiv preprint arXiv:0905.2166 (2009). [9] J.J. Font, J. Galindo, S. Macario, and M. Sanchis, Mazur-Ulam type theorems for fuzzy normed spaces, J. Nonlinear Sci. Appl. 10 (2017), no. 8, 4499–4506. [10] J.J. Font, J. Galindo, S. Macario, and M. Sanchis, A generalized Mazur-Ulam theorem for fuzzy normed spaces, Abstr. Appl. Anal. 2014 (2014), no. 1, 624920. [11] R. Hu, On the maps preserving the equality of distance, J. Math. Anal. Appl. 343 (2008), no.2, 1161–1165. [12] P. Isaac and K. Maya, On the intuitionistic normed linear space (Rn, A), Fuzzy Math. Syst. 2 (2012), 95–110. [13] D. Kang, H. Koh, and I.G. Cho, On the Mazur–Ulam theorem in non-Archimedean fuzzy normed spaces, Appl. Math. Lett. 25 (2012), no. 3, 301–304. [14] I. Kramosil and J. Michalek., Fuzzy metrics and statistical metric spaces, Kybernetika 11 (1975), no. 5, 336–344. [15] S. Mazur and S. Ulam, Sur les transformations isom´etriques d’espaces vectoriels norm´es, CR Acad. Sci. Paris 194 (1932), no. 946–948. [16] J.H. Park, Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals 22 (2004), no. 5, 1039–1046. [17] C. Park and C. Alaca., Mazur-Ulam theorem under weaker conditions in the framework of 2-fuzzy 2-normed linear spaces, J. Inequal. Appl. 2013 (2013), no. 1, 1–9. [18] A. Pourmoslemi and K. Nourouzi, Mazur-Ulam theorem in probabilistic normed groups, Int. J. Nonlinear Anal. Appl. 8 (2017), no. 2, 327–333. [19] R. Saadati and J.H. Park., On the intuitionistic fuzzy topological spaces, Chaos Solitons Fractals 27 (2006), no. 2, 331–344. [20] T.K. Samanta and I.H. Jebril, Finite dimensional intuitionistic fuzzy normed linear space, Int. J. Open Prob. Compt. Math. 2 (2009), no. 4, 574–591. [21] W. Shatanawi and M. Postolache, Mazur-Ulam theorem for probabilistic 2-normed spaces, J. Nonlinear Sci. Appl. 8 (2015), no. 6, 1228–1233. [22] E. Szmidt and J. Kacprzyk, Distances between intuitionistic fuzzy sets, Fuzzy Sets Syst. 114 (2000), no. 3, 505–518. [23] J. Vaisala, A proof of the Mazur-Ulam theorem, Amer. Math. Monthly 110 (2003), no. 7, 633–635. [24] A. Vogt, Maps which preserve equality of distance, Studia Math. 45 (1973), no. 1, 43–48. [25] A.L. Zadeh, Fuzzy sets, Inf. Control 8 (1965), no. 3, 338–353. | ||
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