New Integral Mean Estimates for the Polar Derivative of a Polynomial
- Authors: Qasim I.1
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Affiliations:
- Government Girls Higher Secondary School Langate
- Issue: Vol 39, No 9 (2018)
- Pages: 1407-1418
- Section: Part 2. Special issue “Actual Problems of Algebra and Analysis” Editors: A. M. Elizarov and E. K. Lipachev
- URL: https://journals.rcsi.science/1995-0802/article/view/203479
- DOI: https://doi.org/10.1134/S1995080218090445
- ID: 203479
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Abstract
Let p(z) be a polynomial of degree n and for α ∈ C, let Dαp(z):= np(z) + (α − z)p′(z) denote the polar derivative of the polynomial p(z) with respect to α. In this paper, we obtain certain integral inequalities concerning the polar derivative of a polynomial, which besides yielding some interesting results, also includes some well-known theorems as special cases. Moreover we refine some Zygmund type inequalities for the polar derivative of a polynomial and present compact generalizations of some prior results.
Keywords
About the authors
Idrees Qasim
Government Girls Higher Secondary School Langate
Author for correspondence.
Email: idreesf3@gmail.com
India, Baramulla-Handwara Rd., Langait, 193302