Displaying similar documents to “On local and global moduli of convexity”

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.

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 minimal points

Gliceria Godini (1980)

Commentationes Mathematicae Universitatis Carolinae

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