On Random Uniform Convexity

We consider convex functions in d real variables. For applications, for example in optimization, various strengthened forms of convexity have been introduced. Among them, uniform convexity is one of the most general, defined by involving a so-called modulus ?. Inspired by three classical characterizations of ordinary convexity, we aim at characterizations of uniform convexity by conditions in terms of the gradient or the Hessian matrix of the considered function for certain classes of moduli ?.

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Bellman function approach to the sharp constants in uniform convexity

Advances in Calculus of Variations ◽

10.1515/acv-2016-0008 ◽

2018 ◽

Vol 11 (1) ◽

pp. 89-93

Author(s):

Paata Ivanisvili

Keyword(s):

Uniform Convexity ◽

Function Approach ◽

Function Technique ◽

Bellman Function ◽

Sharp Constants

AbstractWe illustrate a Bellman function technique in finding the modulus of uniform convexity of {L^{p}} spaces.

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Optimal Two—Uniform Convexity and Fermion Hypercontractivity

Quantum and Non-Commutative Analysis ◽

10.1007/978-94-017-2823-2_7 ◽

1993 ◽

pp. 93-111

Author(s):

Eric A. Carlen ◽

Elliott H. Lieb

Keyword(s):

Uniform Convexity

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Measures of noncompactness and related properties

Elements of Geometry of Balls in Banach Spaces ◽

10.1093/oso/9780198827351.003.0010 ◽

2018 ◽

pp. 128-146

Author(s):

Kazimierz Goebel ◽

Stanisław Prus

Keyword(s):

Uniform Convexity ◽

Measures Of Noncompactness

Attempts to classify properties of the ball B, or the space X, utilizing the notion of measures of noncompactness are presented. They are connected with the Kadec–Klee property. Measures of noncompactness are used to generalize the notion of uniform convexity and smoothness.

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