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E-ISSN: 2788-9327

P-ISSN: 1606-8947

Vol. 27 No. 2 (2023)

Integral Inequalities for the Polar derivative and the generalized Polar derivative of complex Polynomials

  • Adeeb Tawfik Hasson Al-Saeedi Department of Mathematics, Faculty of Education Aden, University of Aden, Aden, Yemen
  • Dhekra Mohammed Mohsen Algawi Department of Mathematics, Faculty of Education Aden, University of Aden, Aden, Yemen

University of Aden Journal of Natural and Applied Sciences, Vol. 27 No. 2 (2023), 31-10-2023

DOI:

https://doi.org/10.47372/uajnas.2023.n2.a11

Abstract

For a polynomial P(z) of degree n , having all zeros in |z|≤1, Malik [11] proved that for each q>0,
\(n [∫_0^{2π} |P(e^{iθ})|^q dθ] ^{1⁄q} ≤[∫_0^{2π} | 1 + e^{iθ} |^q dθ]^{1⁄q} \underset{|z|=1}{max} |P^ʹ (z)|\). In this paper we generalize the above inequality to polar derivative and generalized polar derivative, which as special cases include several known results in this area.

Keywords:
    Polynomials, Restricted Zeros, Inequalities in the Complex Domain

How to Cite

Al-Saeedi , A. T. H., & Algawi, D. M. M. (2023). Integral Inequalities for the Polar derivative and the generalized Polar derivative of complex Polynomials. University of Aden Journal of Natural and Applied Sciences, 27(2). https://doi.org/10.47372/uajnas.2023.n2.a11
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