V. Markov's problem for $k$-absolutely monotone polynomials and applications

Research output: Contribution to journalArticle (Academic Journal)peer-review

Abstract

We consider the classical problem of maximizing the value of the derivative of a
polynomial at a given point x0 ∈ [−1, 1]. The corresponding extremal problem for
general polynomials in the uniform norm was solved by V. Markov. In this paper,
we consider the analog of this problem for k-absolutely monotone polynomials. As a
consequence, we solve the analog of V. Markov’s problem, find the exact constant in
Bernstein’s inequality and give a new proof of A. Markov’s inequality for monotone
polynomials
Original languageEnglish
Pages (from-to)139-149
Number of pages11
JournalJaen Journal on Approximation
Volume11
Issue number1-2
Publication statusPublished - 31 Dec 2019

Keywords

  • Markov’s inequality
  • Nikolskii inequality
  • k-absolutely monotone polynomials
  • shape-preserving approximation

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