Journal of Function Spaces and Applications (Jan 2013)

On the Aleksandrov-Rassias Problems on Linear n-Normed Spaces

  • Yumei Ma

DOI
https://doi.org/10.1155/2013/394216
Journal volume & issue
Vol. 2013

Abstract

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This paper generalizes T. M. Rassias' results in 1993 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→Y preserving unit distance in both directions and preserving any integer distance is an n-isometry.