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oai:docta.ucm.es:20.500.14352/502122025-04-07T18:27:26Zcom_20.500.14352_14col_20.500.14352_15

An application of the Krein-Milman theorem to Bernstein and Markov inequalities Muñoz-Fernández, Gustavo A. Sarantopoulos, Yannis Seoane Sepúlveda, Juan Benigno 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. 2023-06-20T09:42:10Z 2023-06-20T09:42:10Z 2023-06-20T09:42:10Z 2008 journal article https://hdl.handle.net/20.500.14352/50212 0944-6532 eng 2006-03531 restricted access Heldermann Verlag