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Extreme points of the Besicovitch-Orlicz space of almost periodic functions equipped with Orlicz norm

Boulahia Fatiha, Hassaine Slimane

Opuscula Mathematica

2021

Vol. 41, no. 5

629--648

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.

The generalized sine function and geometrical properties of normed spaces

Szostok T.

Opuscula Mathematica

2015

Vol. 35, no. 1

117--126

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.

Twice Differentiable Characterizations of Convexity Notions for Functions on Full Dimensional Convex Sets

Stein O.

Schedae Informaticae

2012

Vol. 21

55--63

We derive C2-characterizations for convex, strictly convex, as well as strongly convex functions on full dimensional convex sets. In the cases of convex and strongly convex functions this weakens the well-known openness assumption on the convex sets. We also show that, in a certain sense, the full dimensionality assumption cannot be weakened further. In the case of strictly convex functions we weaken the well-known sufficient C2-condition for strict convexity to a characterization. Several examples illustrate the results.

Heron's formula in inner product spaces

White A., Cho Y., Kim S.

Demonstratio Mathematica

1998

Vol. 31, nr 1

97-102

In this paper, we given Heron's formula in inner product spa