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Muñoz-Fernández, Gustavo A. and Sarantopoulos, Yannis and Seoane-Sepúlveda, Juan B.
(2008)
*An application of the Krein-Milman theorem to Bernstein and Markov inequalities.*
Journal of Convex Analysis, 15
(2).
pp. 299-312.
ISSN 0944-6532

PDF
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Official URL: http://www.heldermann-verlag.de/jca/jca15/jca0740_b.pdf

## Abstract

Given a trinomial of the form p(x) = ax(m) + bx(n) + c with a, b, c is an element of R, we obtain, explicitly, the best possible constant M.,,(x) in the inequality vertical bar p'(x)vertical bar <= M-m,M-n(x).parallel to p parallel to, where x is an element of [-1, 1] is fixed and parallel to p parallel to is the sup norm of p over [-1, 1]. This answers a question to an old problem, first studied by Markov, for a large family of trinomials. We obtain the mappings M-m,M-n(x) by means of classical convex analysis techniques, in particular, using the Krein-Milman approach.

Item Type: | Article |
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Uncontrolled Keywords: | Bernstein and Markov inequalies; trinomials; extreme points |

Subjects: | Sciences > Mathematics > Numerical analysis |

ID Code: | 17232 |

Deposited On: | 28 Nov 2012 09:26 |

Last Modified: | 16 Nov 2018 17:54 |

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