1,131 research outputs found
On the Mazur--Ulam theorem in fuzzy n--normed strictly convex spaces
In this paper, we generalize the Mazur--Ulam theorem in the fuzzy real
n-normed strictly convex spaces.Comment: 7 page
Equilateral dimension of some classes of normed spaces
An equilateral dimension of a normed space is a maximal number of pairwise
equidistant points of this space. The aim of this paper is to study the
equilateral dimension of certain classes of finite dimensional normed spaces.
The well-known conjecture states that the equilateral dimension of any
-dimensional normed space is not less than . By using an elementary
continuity argument, we establish it in the following classes of spaces:
permutation-invariant spaces, Orlicz-Musielak spaces and in one codimensional
subspaces of . For smooth and symmetric spaces,
Orlicz-Musielak spaces satisfying an additional condition and every
-dimensional subspace of we also provide some weaker
bounds on the equilateral dimension for every space which is sufficiently close
to one of these. This generalizes the result of Swanepoel and Villa concerning
the spaces.Comment: 14 pages, Numerical Functional Analysis and Optimization 35 (2014
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