Geodesic
On a Cosine Function Defined for Smooth Normed Spaces
Journal of convex analysis, Tome 25 (2018) no. 1, pp. 21-39
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We continue research on a certain cosine function defined for smooth Minkowski spaces. We prove that such function is symmetric if and only if the corresponding space is Euclidean, and also that it can be given in terms of the Gateaux derivative of the norm. As an application we study the ratio between the lengths of tangent segments drawn from an external point to the unit circle of a Radon plane. We also give a characterization of such planes in terms of signs of the cosine function.
Classification : 46B20, 33B10, 52A10, 52A21
Mots-clés : Gateaux derivative, Minkowski cosine function, Minkowski geometry, Radon curves, semi-inner product, smooth norm 
@article{JCA_2018_25_1_JCA_2018_25_1_a1,
     author = {V. Balestro and E. Shonoda},
     title = {On a {Cosine} {Function} {Defined} for {Smooth} {Normed} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {21--39},
     year = {2018},
     volume = {25},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2018_25_1_JCA_2018_25_1_a1/}
}
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V. Balestro; E. Shonoda. On a Cosine Function Defined for Smooth Normed Spaces. Journal of convex analysis, Tome 25 (2018) no. 1, pp. 21-39. http://geodesic.mathdoc.fr/item/JCA_2018_25_1_JCA_2018_25_1_a1/