- Tytuł:
- The generalized sine function and geometrical properties of normed spaces
- Autorzy:
- Szostok, T.
- Powiązania:
- https://bibliotekanauki.pl/articles/255087.pdf
- Data publikacji:
- 2015
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
geometry of normed spaces
smoothness
strict convexity
Birkhoff-James orthogonality
conditional functional equations - Opis:
- Let [formula] be a nornied space. We deal here with a function s : X x X —> R given by the formula [formula] (for x = 0 we must define it separately). Then we take two unit vectors x and y such that y is orthogonal to x in the Birkhoff-James sense. Using these vectors we construct new functions Φx,y which are defined on R. If X is an inner product space, then Φx, y = sin and, therefore, one may call this function a generalization of the sine function. We show that the properties of this function are connected with geometrical properties of the normed space X.
- Źródło:
-
Opuscula Mathematica; 2015, 35, 1; 117-126
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł