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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Norm estimates relating polynomials and their derivatives


Author: Zalman Rubinstein
Journal: Proc. Amer. Math. Soc. 80 (1980), 78-82
MSC: Primary 41A17; Secondary 26D10, 30C10
DOI: https://doi.org/10.1090/S0002-9939-1980-0574512-1
MathSciNet review: 574512
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Abstract: Inequalities bounding $ {L_p}(p > 0)$ norms of a polynomial by suitable norms of the derivative of the polynomial and an auxiliary function are obtained for the classes of polynomials whose zeros lie on the unit circumference or in the interior or the exterior of the unit disk. All the inequalities are best possible and generalize several known estimates in particular cases.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0574512-1
Keywords: $ {L_p}$-norm, inequality, C-polynomial
Article copyright: © Copyright 1980 American Mathematical Society

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