Equilateral, diametral, centered sets and subsets of spheres.
On weakly uniformly convex spaces according to Calder.
Bivariate copulas, norms and non-exchangeability
The present paper is related to the study of asymmetry for copulas by introducing functionals based on different norms for continuous variables. In particular, we discuss some facts concerning asymmetry and we point out some flaws occurring in the recent literature dealing with this matter.
Estimates for Kottman's separation constant in reflexive Banach spaces
In reflexive Banach spaces with some degree of uniform convexity, we obtain estimates for Kottman's separation constant in terms of the corresponding modulus.
Quasi-concave copulas, asymmetry and transformations
In this paper we consider a class of copulas, called quasi-concave; we compare them with other classes of copulas and we study conditions implying symmetry for them. Recently, a measure of asymmetry for copulas has been introduced and the maximum degree of asymmetry for them in this sense has been computed: see Nelsen R.B., , Statist. Papers (2007), 329–336; Klement E.P., Mesiar R., ?, Comment. Math. Univ. Carolin. (2006), 141–148. Here we compute the maximum degree of asymmetry that quasi-concave...
Bicontractive projections in sequence spaces and a few related kinds of maps
Componentwise concave copulas and their asymmetry
The class of componentwise concave copulas is considered, with particular emphasis on its closure under some constructions of copulas (e.g., ordinal sum) and its relations with other classes of copulas characterized by some notions of concavity and/or convexity. Then, a sharp upper bound is given for the -measure of non-exchangeability for copulas belonging to this class.
On nested sequences of convex sets in Banach spaces
We study different aspects of the representation of weak*-compact convex sets of the bidual X** of a separable Banach space X via a nested sequence of closed convex bounded sets of X.
On Kottman's constants in Banach spaces
This paper deals with a few, not widely known, aspects of Kottman's constant of a Banach space and its symmetric and finite variations. We will consider their behaviour under ultrapowers, relations with other parameters such as Whitley's or James' constant, and connection with the extension of c₀-valued Lipschitz maps.
Projections, skewness and related constants in real normed spaces.
Diametrically contractive maps and fixed points.
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