On the Aleksandrov problem for mappings preserving fuzzy n-distance in fuzzy n-normed spaces

Article type: Research Article

Authors: Esfahani, Hassan Noori^a | Saadati, Reza^{b; *}

Affiliations: [a] Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran | [b] School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran

Correspondence: [*] Corresponding author. Reza Saadati, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran. E-mail: rsaadati@iust.ac.ir.

Abstract: We study the problem of Aleksandrov in fuzzy n-normed spaces and prove that every surjective fuzzy function preserving unit n-distance is affine, and thus is a fuzzy n-isometry. Finally, we show that every fuzzy function preserving two fuzzy unit n-distances confirmers the result of Benz theorem when target space is fuzzy n-strictly convex.

Keywords: Aleksandrov problem, f-n-UDPP, f-n-NLS, fuzzy n-isometry, f-β-n-distance, f-n-strictly convex

Keywords: 54H20, 46L05, 11Y50

DOI: 10.3233/JIFS-190852

Journal: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 5, pp. 6925-6935, 2019