Volume 29, Issue 1
Some Results Concerning Growth of Polynomials

A. Zireh ,  E. Khojastehnejhad and S. R. Musawi


Anal. Theory Appl., 29 (2013), pp. 37-46

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  • Abstract

Let $P(z)$ be a polynomial of degree $n$ having no zeros in$|z|&It 1$, then for every real or complex number $\beta$ with$|\beta|\leq 1$, and $|z|=1$, $R\geq 1$, it is proved by Dewan etal. [4] that$$\Big|P(Rz)+\beta\Big(\frac{R+1}{2}\Big)^n P(z)\Big|\leq\frac{1}{2}\Big\{\Big(\Big|R^n+\beta\Big(\frac{R+1}{2}\Big)^n\Big|+\Big|1+\beta\Big(\frac{R+1}{2}\Big)^n\Big|\Big)\max_{|z|=1}|P(z)|\\- \Big(\Big|R^n+\beta\Big(\frac{R+1}{2}\Big)^n\Big|-\Big|1+\beta\Big(\frac{R+1}{2}\Big)^n|\Big)\min_{|z|=1}|P(z)|\Big\}.$$ In this paper we generalize the above inequality for polynomials having no zeros in $|z| &It k$, $k\leq 1$. Our resultsgeneralize certain well-known polynomial inequalities.

  • History

Published online: 2013-03

  • AMS Subject Headings

30A10, 30C10, 30E15

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