RT Journal Article
T1 An application of the Krein-Milman theorem to Bernstein and Markov inequalities
A1 Muñoz-Fernández, Gustavo A.
A1 Sarantopoulos, Yannis
A1 Seoane-Sepúlveda, Juan B.
AB 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.
PB Heldermann Verlag
SN 0944-6532
YR 2008
FD 2008
LK https://hdl.handle.net/20.500.14352/50212
UL https://hdl.handle.net/20.500.14352/50212
LA eng
NO MTM
DS Docta Complutense
RD 6 abr 2025