Isometries, Mazur–Ulam theorem and Aleksandrov problem for non-Archimedean normed spaces

Kubzdela, Albert

doi:10.1016/j.na.2011.10.006

Cited by 6 publications

(3 citation statements)

References 9 publications

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“…Also, he gave a new generalization of the Mazur-Ulam theorem when X is a 2-fuzzy 2-normed linear space or I(𝑋) is a fuzzy 2-normed linear space. Kubzdela [10] gave some new results…”

Section: Introductionmentioning

confidence: 97%

“…The classical result of Mazur and Ulam states that if X, Y are real normed linear spaces and 𝑓 : X → Y is a surjective isometry, then 𝑓 is affine; that is, 𝑓 is a linear mapping up to translation. Numerous generalizations of this fact were presented by many authors (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13] and references therein). Unfortunately, the Mazur-Ulam theorem is not true for normed complex vector space.…”

Section: Introductionmentioning

confidence: 99%

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On the Mazur-Ulam Theorem in Non-Archimedean Fuzzy -Normed Spaces

2013

ISRN Mathematical Analysis

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The motivation of this paper is to present a new notion of non-Archimedean fuzzy -normed space over a field with valuation. We obtain a Mazur-Ulam theorem for fuzzy -isometry mappings in the strictly convex non-Archimedean fuzzy -normed spaces. We also prove that the interior preserving mapping carries the barycenter of a triangle to the barycenter point of the corresponding triangle. And then, using this result, we get a Mazur-Ulam theorem for the interior preserving fuzzy -isometry mappings in non-Archimedean fuzzy -normed spaces over a linear ordered non-Archimedean field.

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“…Also, he gave a new generalization of the Mazur-Ulam theorem when X is a 2-fuzzy 2-normed linear space or I(𝑋) is a fuzzy 2-normed linear space. Kubzdela [10] gave some new results…”

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

On the Mazur-Ulam Theorem in Non-Archimedean Fuzzy -Normed Spaces

2013

ISRN Mathematical Analysis

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“…In [9], there was an attempt to prove an ultrametric version of the Mazur-Ulam Theorem introducing the notion of non-Archimedean strictly convex space. Nevertheless, Professor A. Kubzdela observed some years later that non-Archimedean strictly convex spaces are a rarity (see [8]).…”

Section: Introductionmentioning

confidence: 99%

Isometries of ultrametric normed spaces

Sánchez

Navarro

2021

Ann. Funct. Anal.

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We show that the group of isometries of an ultrametric normed space can be seen as a kind of a fractal. Then, we apply this description to study ultrametric counterparts of some classical problems in Archimedean analysis, such as the so called Problème des rotations de Mazur or Tingley’s problem. In particular, it turns out that, in contrast with the case of real normed spaces, isometries between ultrametric normed spaces can be very far from being linear.

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Isometry and phase-isometry of non-Archimedean normed spaces

Wang,

Yao

2023

Acta Math Sci

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Isometries, Mazur–Ulam theorem and Aleksandrov problem for non-Archimedean normed spaces

Cited by 6 publications

References 9 publications

On the Mazur-Ulam Theorem in Non-Archimedean Fuzzy -Normed Spaces

On the Mazur-Ulam Theorem in Non-Archimedean Fuzzy -Normed Spaces

Isometries of ultrametric normed spaces

Isometry and phase-isometry of non-Archimedean normed spaces

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