Cauchy’s Functional Equation, Schur’s Lemma, One-Dimensional Special Relativity, and Möbius’s Functional Equation

Suksumran, Teerapong

doi:10.1007/978-3-319-74325-7_20

Springer Optimization and Its Applications

2018

DOI: 10.1007/978-3-319-74325-7_20

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Cauchy’s Functional Equation, Schur’s Lemma, One-Dimensional Special Relativity, and Möbius’s Functional Equation

Teerapong Suksumran

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2019

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On Metric Structures of Normed Gyrogroups

Suksumran

2019

Mathematical Analysis and Applications

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In this article, we indicate that the open unit ball in n-dimensional Euclidean space R n admits norm-like functions compatible with the Poincaré and Beltrami-Klein metrics. This leads to the notion of a normed gyrogroup, similar to that of a normed group in the literature. We then examine topological and geometric structures of normed gyrogroups. In particular, we prove that the normed gyrogroups are homogeneous and form left invariant metric spaces and derive a version of the Mazur-Ulam theorem. We also give certain sufficient conditions, involving the right-gyrotranslation inequality and Klee's condition, for a normed gyrogroup to be a topological gyrogroup.

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On Metric Structures of Normed Gyrogroups

Suksumran

2019

Mathematical Analysis and Applications

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Cauchy’s Functional Equation, Schur’s Lemma, One-Dimensional Special Relativity, and Möbius’s Functional Equation

Cited by 1 publication

References 7 publications

On Metric Structures of Normed Gyrogroups

On Metric Structures of Normed Gyrogroups

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