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SUCCESSIVE RADII OF FAMILIES OF CONVEX BODIES

Published online by Cambridge University Press:  15 December 2014

BERNARDO GONZÁLEZ
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100-Murcia, Spain email bgmerino@gmail.com
MARÍA A. HERNÁNDEZ CIFRE*
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain email mhcifre@um.es
AICKE HINRICHS
Affiliation:
Institut für Analysis, Johannes Kepler Universität Linz, Altenberger Str. 69, 4040 Linz, Austria email aicke.hinrichs@jku.at
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Abstract

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We study properties of the so-called inner and outer successive radii of special families of convex bodies. First we consider the balls of the $p$-norms, for which we show that the precise value of the outer (inner) radii when $p\geq 2$ ($1\leq p\leq 2$), as well as bounds in the contrary case $1\leq p\leq 2$ ($p\geq 2$), can be obtained as consequences of known results on Gelfand and Kolmogorov numbers of identity operators between finite-dimensional normed spaces. We also prove properties that successive radii satisfy when we restrict to the families of the constant width sets and the $p$-tangential bodies.

Type
Research Article
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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