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An application of the Krein-Milman theorem to Bernstein and Markov inequalities

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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

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


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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
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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