3 results
Isometry on Linear n-G-quasi Normed Spaces
-
- Journal:
- Canadian Mathematical Bulletin / Volume 60 / Issue 2 / 01 June 2017
- Published online by Cambridge University Press:
- 20 November 2018, pp. 350-363
- Print publication:
- 01 June 2017
-
- Article
-
- You have access
- Export citation
-
This paper generalizes the Aleksandrov problem: the Mazur-Ulam theorem on
$n-G$-quasi normed spaces. It proves that a one-
$n$-distance preserving mapping is an $n$-isometry if and only if it has the zero-$n-G$-quasi preserving property, and two kinds of $n$-isometries on $n-G$-quasi normed space are equivalent; we generalize the Benz theorem to $n$-normed spaces with no restrictions on the dimension of spaces.
MAPPINGS OF CONSERVATIVE DISTANCES IN
$p$-NORMED SPACES (
$0<p\leq 1$)
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 95 / Issue 2 / April 2017
- Published online by Cambridge University Press:
- 02 November 2016, pp. 291-298
- Print publication:
- April 2017
-
- Article
-
- You have access
- Export citation
-
We show that any mapping between two real
$p$-normed spaces, which preserves the unit distance and the midpoint of segments with distance 
$2^{p}$, is an isometry. Making use of it, we provide an alternative proof of some known results on the Aleksandrov question in normed spaces and also generalise these known results to 
$p$-normed spaces.
ON THE ALEKSANDROV–RASSIAS PROBLEM OF DISTANCE PRESERVING MAPPINGS
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 91 / Issue 3 / June 2015
- Published online by Cambridge University Press:
- 17 March 2015, pp. 464-470
- Print publication:
- June 2015
-
- Article
-
- You have access
- Export citation
