DOI QR코드

DOI QR Code

THE ALEKSANDROV PROBLEM AND THE MAZUR-ULAM THEOREM ON LINEAR n-NORMED SPACES

  • Yumei, Ma (Department of Mathematics Dalian Nationality University)
  • 투고 : 2012.09.29
  • 발행 : 2013.09.30

초록

This paper generalizes the Aleksandrov problem and Mazur Ulam theorem to the case of $n$-normed spaces. For real $n$-normed spaces X and Y, we will prove that $f$ is an affine isometry when the mapping satisfies the weaker assumptions that preserves unit distance, $n$-colinear and 2-colinear on same-order.

참고문헌

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피인용 문헌

  1. The Aleksandrov–Benz–Rassias problem on linear n-normed spaces vol.180, pp.2, 2016, https://doi.org/10.1007/s00605-015-0786-8
  2. Isometry on Linear n-G-quasi Normed Spaces vol.60, pp.02, 2017, https://doi.org/10.4153/CMB-2016-061-9