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Integral Mean Estimates for a Polynomial with Restricted Zeros

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Book cover Current Topics in Pure and Computational Complex Analysis

Part of the book series: Trends in Mathematics ((TM))

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Abstract

In this paper, we prove some \(L^{q},~q\ge 0\) mean inequalities for a class of polynomials

$$\begin{aligned} \textbf{P}_{n,\mu}:=\bigg\{P(z)=a_{n}z^{n}+\sum\limits_{j=\mu}^{n}a_{n-j}z^{n-j},~~1\le\mu\le n\bigg\}\end{aligned}$$

having all zeros in \(|z|\le k,~k\le 1.\)

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Author information

Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Kashmir, 190006, India

    A. Liman

  2. Jammu and Kashmir Institute of Mathematical Sciences, Srinagar, 190008, India

    W. M. Shah

Authors
  1. A. Liman
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  2. W. M. Shah
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Correspondence to A. Liman .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Walchand College of Engineering, Sangli, Maharashtra, India

    Santosh Joshi

  2. Department of Mathematics, Brigham Young University, Provo, Utah, USA

    Michael Dorff

  3. Department of Mathematics, University of Kalyani, Kalyani, West Bengal, India

    Indrajit Lahiri

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Liman, A., Shah, W. (2014). Integral Mean Estimates for a Polynomial with Restricted Zeros. In: Joshi, S., Dorff, M., Lahiri, I. (eds) Current Topics in Pure and Computational Complex Analysis. Trends in Mathematics. Birkhäuser, New Delhi. https://doi.org/10.1007/978-81-322-2113-5_11

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