scholarly journals On the Aleksandrov-Rassias Problems on Linearn-Normed Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Yumei Ma
Keyword(s):  
Normed Spaces ◽  
Unit Distance ◽  
Strictly Convex ◽  
Surjective Mapping

This paper generalizes T. M. Rassias' results in 1993 ton-normed spaces. IfXandYare two realn-normed spaces andYisn-strictly convex, a surjective mappingf:X→Ypreserving unit distance in both directions and preserving any integer distance is ann-isometry.

Strictly Convex Linear 2-Normed Spaces

1990 ◽  
Vol 146 (1) ◽  
pp. 7-16 ◽  
Author(s):  
Ki Sik Ha ◽  
Yeol Je Cho ◽  
Seong Sik Kim ◽  
M. S. Khan
Keyword(s):  
Normed Spaces ◽  
Strictly Convex

Strictly Convex Linear 2-Normed Spaces

1974 ◽  
Vol 59 (1-6) ◽  
pp. 319-324 ◽  
Author(s):  
Charles Diminnie ◽  
Siegfried Gähler ◽  
Albert White
Keyword(s):  
Normed Spaces ◽  
Strictly Convex

On Wigner's theorem in strictly convex normed spaces

2020 ◽  
Vol 97 (3-4) ◽  
pp. 393-401 ◽  
Author(s):  
Dijana Ilisevic ◽  
Aleksej Turnsek
Keyword(s):  
Normed Spaces ◽  
Strictly Convex ◽  
Wigner’S Theorem ◽  
Wigner's Theorem

scholarly journals On normed spaces with the Wigner Property

2019 ◽  
Vol 11 (3) ◽  
pp. 523-539 ◽  
Author(s):  
Ruidong Wang ◽  
Dariusz Bugajewski
Keyword(s):  
Normed Space ◽  
Two Dimensional ◽  
Normed Spaces ◽  
Strictly Convex ◽  
Real Normed Space

AbstractThe aim of this paper is to generalize the Wigner Theorem to real normed spaces. A normed space is said to have the Wigner Property if the Wigner Theorem holds for it. We prove that every two-dimensional real normed space has the Wigner Property. We also study the Wigner Property of real normed spaces of dimension at least three. It is also shown that strictly convex real normed spaces possess the Wigner Property.

scholarly journals Which graphs are rigid in $$\ell _p^d$$?

2021 ◽  
Author(s):  
Sean Dewar ◽  
Derek Kitson ◽  
Anthony Nixon
Keyword(s):  
Projective Plane ◽  
General Class ◽  
Maximum Degree ◽  
Minimum Degree ◽  
Sparse Graph ◽  
Normed Spaces ◽  
3 Dimensional ◽  
Strictly Convex ◽  
Generic Rigidity

AbstractWe present three results which support the conjecture that a graph is minimally rigid in d-dimensional $$\ell _p$$ ℓ p -space, where $$p\in (1,\infty )$$ p ∈ ( 1 , ∞ ) and $$p\not =2$$ p ≠ 2 , if and only if it is (d, d)-tight. Firstly, we introduce a graph bracing operation which preserves independence in the generic rigidity matroid when passing from $$\ell _p^d$$ ℓ p d to $$\ell _p^{d+1}$$ ℓ p d + 1 . We then prove that every (d, d)-sparse graph with minimum degree at most $$d+1$$ d + 1 and maximum degree at most $$d+2$$ d + 2 is independent in $$\ell _p^d$$ ℓ p d . Finally, we prove that every triangulation of the projective plane is minimally rigid in $$\ell _p^3$$ ℓ p 3 . A catalogue of rigidity preserving graph moves is also provided for the more general class of strictly convex and smooth normed spaces and we show that every triangulation of the sphere is independent for 3-dimensional spaces in this class.

Strictly convex n-normed spaces and benz theorem

2017 ◽  
Vol 20 (5) ◽  
pp. 1241-1254
Author(s):  
Xujian Huang ◽  
Xinkun Wang ◽  
Ruidong Wang
Keyword(s):  
Normed Spaces ◽  
Strictly Convex
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