30c15, General Mathematics, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, QA1-939, 30c10, rouche’s theorem, 30a10, Mathematics, sth derivative of a polynomial, lγ inequalities
Abstract
The goal of this paper is to generalize and refine some previous inequalities between the LP- norms of the sth derivative and of the polynomial itself, in the case when the zeros are outside of the open unit disk.
In this paper we prove a recent conjecture formulated by Dmitrishin, Smorodin and Stokolos about that certain polynomials are univalent in the unit disk. As a consequence we get an upper estimate for the Koebe radius of univalent polynomials., Comment: These results was obtained by Brandt M., Variationsmethoden f\"ur in der Einheitskreisscheibe schlichte Polynome, Dissertation, Humboldt-Univ. Berlin, 1987
Pure mathematics, General Mathematics, 010102 general mathematics, 30A10, 010103 numerical & computational mathematics, Type (model theory), 01 natural sciences, 30C10, polar derivative, 30C15, Derivative (finance), Polar, 0101 mathematics, Zygmund inequality, Mathematics
Abstract
In this paper, we present an integral inequality for the polar derivative of polynomials. Our theorem includes as special cases several interesting generalizations of some Zygmund type inequalities for polynomials.
Published
2016
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