Browsing by Subject "strict convexity"

Now showing 1 - 4 of 4

Access status: Open Access ,
Extreme points of the Besicovitch-Orlicz space of almost periodic functions equipped with Orlicz norm
(Wydawnictwa AGH, 2021) Boulahia, Fatiha; Hassaine, Slimane
In the present paper, we give criteria for the existence of extreme points of the Besicovitch-Orlicz space of almost periodic functions equipped with Orlicz norm. Some properties of the set of attainable points of the Amemiya norm in this space are also discussed.
Access status: Restricted ,
Geometryczne własności przestrzeni $L^{p}$
(Data obrony: 2015-09-14) Mulewicz, Bartłomiej
Wydział Matematyki Stosowanej
Access status: Restricted ,
Najlepsza koaproksymacja w przestrzeniach liniowych unormowanych
(Data obrony: 2013-12-19) Wilczek, Barbara
Wydział Matematyki Stosowanej
Access status: Open Access ,
The generalized sine function and geometrical properties of normed spaces
(2015) Szostok, Tomasz
Let $(X,\|\cdot\|)$ be a normed space. We deal here with a function $s:X\times X\to\mathbb{R}$ given by the formula $s(x,y):=\inf_{\lambda\in\mathbb{R}}\frac{\|x+\lambda y\|}{\|x\|}$ (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 $\phi_{x,y}$ which are defined on $\mathbb{R}$. If $X$ is an inner product space, then $\phi_{x,y}=\sin$ 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 $X$.