Abstract
Establishing Markov-type inequalities for the derivatives of polynomials with restricted zeros was initiated by P. Erdös [3] in 1940. Since then several authors proved similar estimates for the derivatives of polynomials of special type. In this paper we work on [−1, 1] and obtain Markov-type estimates for the derivatives of polynomials from a rather wide family of classes of constrained polynomials. In some cases the results turn out to be sharp.
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R. J. Duffin, A. C. Schaeffer (1941):A refinement of an inequality of the brothers Markoff. Trans. Amer. Math. Soc.,40:517–528.
T. Erdèlyi, J. Szabados (1988):On polynomials with positive coefficients. J. Approx. Theory,54:107–122.
P. Erdös (1940):On extremal properties of the derivatives of polynomials. Ann. of Math.,2:310–313.
P. Erdös (1961):Problems and results on the theory of interpolation, II. Acta Math. Hungar.,12:235–244.
G. G. Lorentz (1963):The degree of approximation by polynomials with positive coefficients. Math. Ann.,151:239–251.
A. Markov (1882):Sur une question posée par Mendeleieff. Bull. Acad. Sci. St. Petersburg,62:1–24.
W. Markov (1916):Über Polynome, die in einen gegebenen Intervale moglichst wenig von Null abweichen. Math. Ann.,77:213–258. (The original appeared in Russian in 1892.)
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Communicated by George G. Lorentz.
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Erdèlyi, T. Markov-type estimates for certain classes of constrained polynomials. Constr. Approx 5, 347–356 (1989). https://doi.org/10.1007/BF01889614
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DOI: https://doi.org/10.1007/BF01889614