Geodesic
Inequalities for Polynomials with a Prescribed Zero
Canadian journal of mathematics, Tome 34 (1982) no. 3, pp. 737-740

Voir la notice de l'article provenant de la source Cambridge University Press

If P(z) is a polynomial of degree n, then the inequality 1 is trivial. It was asked by Callahan [1], what improvement results from supposing that P(z) has a zero on |z| = 1 and he answered the question by showing that if P( l ) = 0, then 2 Donaldson and Rahman [3] have shown that if P(z) is a polynomial of degree n such that P(β) = 0 where β is an arbitrary non-negative number, then 3 whereas if the polynomial P(z) is such that P(l) = 0, then [4] 4 
Aziz, Abdul. Inequalities for Polynomials with a Prescribed Zero. Canadian journal of mathematics, Tome 34 (1982) no. 3, pp. 737-740. doi: 10.4153/CJM-1982-050-7
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[1] 1. Callahan, F. P., Jr., An extremal problem for polynomials, Proc. Amer. Math. Soc. 10 (1959), 754–755. Google Scholar

[2] 2. Van Der Corput, J. G. and Visser, C., Inequalities concerning polynomials and trigonometric polynomials, Nederl. Akad Wetensch., Proc. 49 (1946), 383–392. Google Scholar

[3] 3. Donaldson, J. D. and Rahman, Q. I., Inequalities for polynomials with a prescribed zero, Pacific J. Math. 41 (1972), 375–378. Google Scholar

[4] 4. Rahman, Q. I. and Mohammad, Q. G., Remarks on Schwarz’ slemma, Pacific J. Math. 28 (1967), 139–142. Google Scholar

[5] 5. Szasz, O., Elementare extremal problème uber nicht negative trigonometrische polynôme, Bayer, S. B.. Akad. Wiss. Math. Phys. Kl. (1927), 185–196. Google Scholar

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