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L-P-Analogues of Bernstein and Markov Inequalities

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Muñoz-Fernández, Gustavo A. y Sánchez, V.M. y Seoane-Sepúlveda, Juan B. (2011) L-P-Analogues of Bernstein and Markov Inequalities. Mathematical Inequalities & Applications, 14 (1). pp. 135-145. ISSN 1331-4343

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Let parallel to . parallel to(infinity) denote the sup norm on [-1,1]. If x is an element of [-1,1] is fixed and M-m,M-n(x) is the best constant in vertical bar p'(x)vertical bar <= M-m,M-n(x)parallel to p parallel to(infinity), for all trinomials p of the form p(x) = ax(m) + bx(n) + c with a, b, c is an element of R, then the exact value of M-m,M-n(x) is known for large families of pairs (m,n) is an element of N-2. Here we consider the same problem for L-p-norms.


Tipo de documento:Artículo
Palabras clave:Bernstein and Markov type inequality; trinomial
Materias:Ciencias > Matemáticas > Funciones (Matemáticas)
Código ID:16897
Referencias:

S. BERNSTEIN, Sur L’ordre de la meilleure approximation des fonctions continues par des polynomes de degr´e donn´e, Memoires de l’Acad´emie Royale de Belgique, 4 (1912), 1–103.

R. P. BOAS, Inequalities for the derivatives of polynomials, Math. Mag., 42 (1969), 165–174.

P. BORWEIN AND T. ERDÉLYI, Polynomials and polynomial inequalities, Graduate Texts in Mathematics, 161, Springer-Verlag, New York, 1995.

R. J. DUFFIN AND A. C. SCHAEFFER, On some inequalities of S. Bernstein and W. Markoff, Bull. Amer. Math. Soc., 44 (1938), 289–297.

L. A. HARRIS, Bounds on the derivatives of holomorphic functions of vectors, Colloque D’Analyse (Rio de Janeiro, 1972), 145–163, ed. L. Nachbin, Act. Sc. et Ind., 1367, Herman, Paris, 1975.

L. A. HARRIS, Multivariate Markov polynomial inequalities and Chebyshev nodes, J. Math. Anal. Appl., 338 (2008), 350–357.

A. A. MARKOV, On a problem of D. I. Mendeleev (Russian), Zap. Im. Akad. Nauk., 62 (1889), 1–24.

A. A. MARKOV, On a question by D. I. Mendeleev, Electronic article to downloaded from http://www.math.technion.ac.il/hat/papers.html.

V. MARKOV, Über Polynome, die in einen gegebenen Intervalle möglichst wenig von Null abweichen, Math. Ann. 77 (1916), 213–258.

G. A. MUÑOZ-FERNÁNDEZ AND Y. SARANTOPOULOS, Bernstein and Markov-type inequalities for polynomials on real Banach spaces, Math. Proc. Camb. Phil. Soc., 133 (2002), 515–530.

G. A. MUÑOZ-FERNÁNDEZ AND J.B. SEOANE-SEPÚLVEDA, Geometry of Banach spaces of Trinomials, J. Math. Anal. Appl., 340 (2008), 1069–1087.

G. A. MUÑOZ-FERNÁNDEZ, Y. SARANTOPOULOS AND J.B. SEOANE-SEPÚLVEDA,An application of the Krein-Milman Theorem to Bernstein and Markov inequalities, J. Convex Anal., 15 (2008), 299–312.

G. A. MUÑOZ-FERNÁNDEZ, V.M. SÁNCHEZ AND J.B. SEOANE-SEPÚLVEDA, Estimates on the derivative of a polynomial with a curved majorant using convex techniques, J. Convex Anal., 17 (2010) 241–252.

S. NEUWIRTH, The maximum modulus of a trigonometric trinomial, J. Anal. Math., 104 (2008), 371–396.

Q. I. RAHMAN, On a problem of Turán about polynomials with curved majorants, Trans.Amer.Math.Soc., 163 (1972), 447–455.

Q. I. RAHMAN AND G. SCHMEISSER,Analytic theory of polynomials, London Mathematical Society Monographs. New Series, 26. The Clarendon Press, Oxford University Press, Oxford, 2002.

Y. SARANTOPOULOS,Bounds on the derivatives of polynomials on Banach spaces, Math. Proc. Camb. Phil. Soc., 110 (1991), 307–312.

V. I. SKALYGA, Analogues of the Markov and Bernstein inequalities for polynomials in Banach spaces, Izv. Math., 61 (1998), 143–159.

V. I. SKALYGA, Analogues of the Markov and Benstein inequalities on convex bodies in Banach spaces, Izv. Math., 62 (1998), 375–397.

V. I. SKALYGA, Bounds on the derivatives of polynomials on entrally symmetric convex bodies (Russian), Izv. Ross. Akad. Nauk Ser. Mat., 69 (2005), 179–192; translation in Izv. Math., 69 (2005), 607–621.

D. R. WILHELMSEN,A Markov inequality in several dimensions, J. Approx. Theory, 11 (1974), 216–220.

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