Generalizations of Zygmund-type integral inequalities for the polar derivative of a complex polynomial

Generalizations of Zygmund-type integral inequalities for the polar derivative of a complex polynomial

Abstract Some Zygmund-type integral inequalities for the polar derivatives of complex polynomials, inspired by the classical Bernstein-type inequalities that relate the uniform norms of polynomials and their derivatives on the unit circle, are investigated. The obtained results sharpen as well as ge...

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Main Authors: Gradimir V. Milovanović, Abdullah Mir
Format: Article
Language:English
Published: SpringerOpen 2020-05-01
Series:Journal of Inequalities and Applications
Subjects:
Polar derivative
Zygmund-type inequality
Integral norm
Online Access:http://link.springer.com/article/10.1186/s13660-020-02404-x
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spelling doaj-a8acde4fde3e4f8086a04ffd652edcc22020-11-25T02:15:00ZengSpringerOpenJournal of Inequalities and Applications1029-242X2020-05-012020111210.1186/s13660-020-02404-xGeneralizations of Zygmund-type integral inequalities for the polar derivative of a complex polynomialGradimir V. Milovanović0Abdullah Mir1Serbian Academy of Sciences and ArtsDepartment of Mathematics, University of KashmirAbstract Some Zygmund-type integral inequalities for the polar derivatives of complex polynomials, inspired by the classical Bernstein-type inequalities that relate the uniform norms of polynomials and their derivatives on the unit circle, are investigated. The obtained results sharpen as well as generalize some already known L δ $L^{\delta }$ -estimates between polynomials and their polar derivatives.http://link.springer.com/article/10.1186/s13660-020-02404-xPolar derivativeZygmund-type inequalityIntegral norm
collection DOAJ
language English
format Article
sources DOAJ
author Gradimir V. Milovanović
Abdullah Mir
spellingShingle Gradimir V. Milovanović
Abdullah Mir
Generalizations of Zygmund-type integral inequalities for the polar derivative of a complex polynomial
Journal of Inequalities and Applications
Polar derivative
Zygmund-type inequality
Integral norm
author_facet Gradimir V. Milovanović
Abdullah Mir
author_sort Gradimir V. Milovanović
title Generalizations of Zygmund-type integral inequalities for the polar derivative of a complex polynomial
title_short Generalizations of Zygmund-type integral inequalities for the polar derivative of a complex polynomial
title_full Generalizations of Zygmund-type integral inequalities for the polar derivative of a complex polynomial
title_fullStr Generalizations of Zygmund-type integral inequalities for the polar derivative of a complex polynomial
title_full_unstemmed Generalizations of Zygmund-type integral inequalities for the polar derivative of a complex polynomial
title_sort generalizations of zygmund-type integral inequalities for the polar derivative of a complex polynomial
publisher SpringerOpen
series Journal of Inequalities and Applications
issn 1029-242X
publishDate 2020-05-01
description Abstract Some Zygmund-type integral inequalities for the polar derivatives of complex polynomials, inspired by the classical Bernstein-type inequalities that relate the uniform norms of polynomials and their derivatives on the unit circle, are investigated. The obtained results sharpen as well as generalize some already known L δ $L^{\delta }$ -estimates between polynomials and their polar derivatives.
topic Polar derivative
Zygmund-type inequality
Integral norm
url http://link.springer.com/article/10.1186/s13660-020-02404-x
work_keys_str_mv AT gradimirvmilovanovic generalizationsofzygmundtypeintegralinequalitiesforthepolarderivativeofacomplexpolynomial
AT abdullahmir generalizationsofzygmundtypeintegralinequalitiesforthepolarderivativeofacomplexpolynomial
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