Displaying similar documents to “On regularization in superreflexive Banach spaces by infimal convolution formulas”

A Clarke–Ledyaev Type Inequality for Certain Non–Convex Sets

Ivanov, M., Zlateva, N. (2000)

Serdica Mathematical Journal

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We consider the question whether the assumption of convexity of the set involved in Clarke-Ledyaev inequality can be relaxed. In the case when the point is outside the convex hull of the set we show that Clarke-Ledyaev type inequality holds if and only if there is certain geometrical relation between the point and the set.

On Uniformly Convex and Uniformly Kadec-Klee Renomings

Lancien, Gilles (1995)

Serdica Mathematical Journal

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We give a new construction of uniformly convex norms with a power type modulus on super-reflexive spaces based on the notion of dentability index. Furthermore, we prove that if the Szlenk index of a Banach space is less than or equal to ω (first infinite ordinal) then there is an equivalent weak* lower semicontinuous positively homogeneous functional on X* satisfying the uniform Kadec-Klee Property for the weak*-topology (UKK*). Then we solve the UKK or UKK* renorming problems for...

An extension of Simons' inequality and applications.

Robert Deville, Catherine Finet (2001)

Revista Matemática Complutense

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This article is devoted to an extension of Simons' inequality. As a consequence, having a pointwise converging sequence of functions, we get criteria of uniform convergence of an associated sequence of functions.

Near smoothness of Banach spaces.

Józef Banas, Kishin Sadarangani (1995)

Collectanea Mathematica

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The aim of this paper is to discuss the concept of near smoothness in some Banach sequence spaces.

On the second order derivatives of convex functions on the Heisenberg group

Cristian E. Gutiérrez, Annamaria Montanari (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In the euclidean setting the celebrated Aleksandrov-Busemann-Feller theorem states that convex functions are a.e. twice differentiable. In this paper we prove that a similar result holds in the Heisenberg group, by showing that every continuous ℋ –convex function belongs to the class of functions whose second order horizontal distributional derivatives are Radon measures. Together with a recent result by Ambrosio and Magnani, this proves the existence a.e. of second order horizontal derivatives...