Nikolskii-type estimates for coconvex approximation of functions with one inflection poin

• G. A. Dzyubenko ^[2] ; D. Leviatan ^[1] ; I. A. Shevchuk ^[3]
  1. [1] Tel Aviv University

     Tel Aviv University

     Israel

     
  2. [2] International mathematical center of NAS of Ukraine
  3. [3] National Taras Shevchenko University of Kyiv

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• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 2, Nº. 1, 2010, págs. 51-64
• Idioma: inglés
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• Resumen

  • For each r ∈ N we prove the Nikolskii type pointwise estimate for coconvex approximation of functions f ∈ Wr, the subspace of all functions f ∈ C[−1, 1], possessing an absolutely continuous (r − 1)st derivative on (−1, 1) and satisfying f(r) ∈ L∞[−1, 1], that change their convexity once on [−1, 1].