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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Main Subjects


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Volume 43, Issue 1
January and February 2017
Pages 163-170
  • Receive Date: 15 July 2015
  • Revise Date: 22 October 2015
  • Accept Date: 23 October 2015