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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

New inequalities for polynomials


Authors: C. Frappier, Q. I. Rahman and St. Ruscheweyh
Journal: Trans. Amer. Math. Soc. 288 (1985), 69-99
MSC: Primary 26D05; Secondary 30A10, 41A17
DOI: https://doi.org/10.1090/S0002-9947-1985-0773048-1
MathSciNet review: 773048
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Abstract: Using a recently developed method to determine bound-preserving convolution operators in the unit disk, we derive various refinements and generalizations of the well-known inequalities of S. Bernstein and M. Riesz for polynomials. Many of these results take into account the size of one or more of the coefficients of the polynomial in question. Other results of similar nature are obtained from a new interpolation formula.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0773048-1
Keywords: Polynomials, Bernstein's inequality, interpolation formula
Article copyright: © Copyright 1985 American Mathematical Society