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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.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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