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Start Over Topic 30c10 Publication Year Range Last 10 years Language undetermined
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1. Some integral inequalities for a polynomial with zeros outside the unit disk

Author

Mir Abdullah

Subjects
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.

Published
2021

2. On a conjecture about univalent polynomials

Author

Kayumov, Ilgiz R. and Khammatova, Diana M.

Subjects
Mathematics - Complex Variables, Mathematics - Classical Analysis and ODEs, Mathematics::Complex Variables, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Complex Variables (math.CV), 30C10
Abstract

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

Published
2020
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3. Polynomials with polar derivatives

Author

Ajaz Wani and Abdullah Mir

Subjects
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