
Journal of Convex Analysis 25 (2018), No. 1, 021039 Copyright Heldermann Verlag 2018 On a Cosine Function Defined for Smooth Normed Spaces Vitor Balestro CEFET/RJ Campus Nova Friburgo, 28635000 Nova Friburgo, Brazil and: Inst. de Matemática e Estatística, Universidade Federal Fluminense, 24020140 Niterói, Brazil vitorbalestro@id.uff.br Emad Shonoda Dept. of Mathematics and Computer Science, Faculty of Science, Port Said University, 42521 Port Said, Egypt en_shonoda@yahoo.de 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. Keywords: Gateaux derivative, Minkowski cosine function, Minkowski geometry, Radon curves, semiinner product, smooth norm. MSC: 46B20; 33B10, 52A10, 52A21 [ Fulltextpdf (155 KB)] for subscribers only. 