Some compact generalization of inequalities for polynomials with prescribed zeros

Document Type : Research Paper

Authors

1 Freelance Mathematics Researcher‎, ‎Mashhad‎, ‎Iran.

2 Department of Mathematics‎, ‎Semnan University‎, ‎Semnan‎, ‎Iran.

Abstract

‎Let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial‎ ‎of degree at most $n-s$ having all its zeros in $|z|\geq k$ or in $|z|\leq k$‎. ‎In this paper we obtain some new results about the dependence of $|p(Rz)|$ on $|p(rz)| $ for $r^2\leq rR\leq k^2$‎, ‎$k^2 \leq rR\leq R^2$ and for $R\leq r \leq k$‎. ‎Our results refine and generalize certain well-known polynomial inequalities‎.

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References

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A. Mir, On extremal properties and location of zeros of polynomials, PhD Thesis, submitted to Jamia Millia Islamia, New Delhi, 2002.
M. S. Pukhta, Extremal problems for polynomials and on location of zeros of polynomials, PhD Thesis, submitted to the Jamia Millia Islamia, New Delhi, 1995.
Bulletin of the Iranian Mathematical Society
Volume 43, Issue 1
February 2017
Pages 163-170

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History

  • Receive Date: 15 July 2015
  • Revise Date: 22 October 2015
  • Accept Date: 23 October 2015

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