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Kolmogorov, Linear and Pseudo-Dimensional Widths of Classes of s-Monotone Functions in 𝕃 p , 0 < p < 1

  • Victor N. Konovalov (a1) and Kirill A. Kopotun (a2)
Abstract

Let Bp be the unit ball in 𝕃 p , 0 < p < 1, and let , s ∈ ℕ, be the set of all s-monotone functions on a finite interval I, i.e., consists of all functions x : I ⟼ ℝ such that the divided differences [x; t 0, … , ts ] of order s are nonnegative for all choices of (s + 1) distinct points t 0, … , ts I. For the classes Bp := Bp, we obtain exact orders of Kolmogorov, linear and pseudo-dimensional widths in the spaces , 0 < q < p < 1:

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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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