## 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

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 language | English |
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Pages (from-to) | 139-149 |

Number of pages | 11 |

Journal | Jaen Journal on Approximation |

Volume | 11 |

Issue number | 1-2 |

Publication status | Published - 31 Dec 2019 |

## Keywords

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