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 |
|---|---|
| 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