On the Aleksandrov-Rassias problems on linear \(n\)-normed spaces
Summary: This paper generalizes results of \textit{Th. M. Rassias} and \textit{P. Šemrl} [Proc. Am. Math. Soc. 118, No. 3, 919--925 (1993; Zbl 0780.51010)] to \(n\)-normed spaces. If \(X\) and \(Y\) are two real \(n\)-normed spaces and \(Y\) is \(n\)-strictly convex, a surjective mapping \(f : X \to Y\) preserving the unit distance in both directions and preserving any integer distance is an \(n\)-isometry.
scientific article; zbMATH DE number 6203149