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Inequalities of Turán-type for algebraic polynomials

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this paper, we establish some new inequalities in the complex plane that are inspired by some classical Turán-type inequalities that relate the norm of a univariate complex coefficient polynomial and its derivative on the unit disk. The obtained results produce various inequalities in the supremum-norm and in the integral-norm of a polynomial that are sharper than the previous ones while taking into account the placement of the zeros and some of the extremal coefficients of the underlying polynomial. Moreover, our results besides derive polar derivative analogues of some classical Turán-type inequalities also include several interesting generalizations and refinements of some integral inequalities for polynomial as well. Some numerical examples are given in order to graphically illustrate and compare the obtained inequalities with some classical results.

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Acknowledgements

The work of G.V. Milovanović was supported in part by Serbian Academy of Sciences and Arts (No. \(\Phi \)-96).

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Authors and Affiliations

  1. Serbian Academy of Sciences and Arts, Kneza Mihaila 35, Beograd, 11000, Serbia

    Gradimir V. Milovanović

  2. Faculty of Science and Mathematics, University of Niš, Niš, 18000, Serbia

    Gradimir V. Milovanović

  3. Department of Mathematics, University of Kashmir, Srinagar, 190006, India

    Abdullah Mir & Adil Hussain

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  1. Gradimir V. Milovanović
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  2. Abdullah Mir
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  3. Adil Hussain
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Correspondence to Gradimir V. Milovanović.

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Milovanović, G.V., Mir, A. & Hussain, A. Inequalities of Turán-type for algebraic polynomials. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 116, 154 (2022). https://doi.org/10.1007/s13398-022-01303-8

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