Displaying similar documents to “Some properties of Pythagorean modulus.”

On the geometry of Banach spaces with modulus of convexity of power type 2

M. Ivanov, A. J. Pallares, S. Troyanski (2010)

Studia Mathematica

Similarity:

We use one-dimensional differential inequalities to estimate the squareness and type of Banach spaces with modulus of convexity of power type two. The estimates obtained are sharp and the constants involved moderate.

Directional moduli of rotundity and smoothness

Michael O. Bartlett, John R. Giles, Jon D. Vanderwerff (1999)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We study various notions of directional moduli of rotundity and when such moduli of rotundity of power type imply the underlying space is superreflexive. Duality with directional moduli of smoothness and some applications are also discussed.

On the local moduli of squareness

Antonio J. Guirao (2008)

Studia Mathematica

Similarity:

We introduce the notions of pointwise modulus of squareness and local modulus of squareness of a normed space X. This answers a question of C. Benítez, K. Przesławski and D. Yost about the definition of a sensible localization of the modulus of squareness. Geometrical properties of the norm of X (Fréchet smoothness, Gâteaux smoothness, local uniform convexity or strict convexity) are characterized in terms of the behaviour of these moduli.

A modulus for property (β) of Rolewicz

J. Ayerbe, T. Domínguez Benavides, S. Cutillas (1997)

Colloquium Mathematicae

Similarity:

We define a modulus for the property (β) of Rolewicz and study some useful properties in fixed point theory for nonexpansive mappings. Moreover, we calculate this modulus in l p spaces for the main measures of noncompactness.