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Growth of polynomials whose zeros are within or outside a circle
Published online by Cambridge University Press: 17 April 2009
Abstract
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Let P (z) be a polynomial of degree n which does not vanish in the disk |z| < K. For K = 1, it is known that
In this paper we consider the two cases K ≥ 1 and K < 1, and present certain generalizations of these results.
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- Copyright © Australian Mathematical Society 1987
References
[1]Aziz, Abdul, “Inequalities for the derivative of a polynomial”, Amer. Math. Soc. 89 (1983), 259–266.CrossRefGoogle Scholar
[2]Aziz, Abdul and Mohammad, Q.G., “Growth of polynomials with zeros outside a circle”, Proc. Amer. Math. Soc. 81 (1981), 549–553.CrossRefGoogle Scholar
[3]Aziz, Abdul and Mohammad, Q.G., “Simple proof of a Theorem of Erdös and Lax”, Proc. Amer. Math. Soc. 80 (1980), 119–122.Google Scholar
[4]Ankeny, N.C. and Rivlin, T.J., “On a theorem of S. Bernstein”, Pacific J. Math. 5 (1955), 849–852.CrossRefGoogle Scholar
[5]Govil, N.K. and Rahman, Q.I., “Functions of exponential type not vanishing in a half-plane and related polynomials”, Trans. Amer. Math. Soc. 137 (1969), 501–517.CrossRefGoogle Scholar
[6]Pólyá, G. and Szegö, G., Aufgaben und Lehrsatze aus der Analysis, Springer-Verlag, Berlin, 1925.Google Scholar
[7]Riesz, M., “Über einen Satz des Herrn Serge Bernstein”, Acta Math. 40 (1916), 337–347.CrossRefGoogle Scholar
[8]Rivlin, T. J., “On the maximum modulus of polynomials”, Amer. Math. Monthly 67 (1960), 251–253.CrossRefGoogle Scholar
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