Displaying similar documents to “On the asymptotic behaviour of a modulus of continuity with discrete description”

Weak moduli of convexity.

Javier Alonso, Antonio Ullán (1991)

Extracta Mathematicae

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Let E be a real normed linear space with unit ball B and unit sphere S. The classical modulus of convexity of J. A. Clarkson [2] δE(ε) = inf {1 - 1/2||x + y||: x,y ∈ B, ||x - y|| ≥ ε} (0 ≤ ε ≤ 2) is well known and it is at the origin of a great number of moduli defined by several authors. Among them, D. F. Cudia [3] defined the directional, weak and directional weak modulus of convexity of E, respectively, as δE...

On the local moduli of squareness

Antonio J. Guirao (2008)

Studia Mathematica

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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.