Anal. Theory Appl., 27 (2011), pp. 150-157.
Published online: 2011-04
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If $p(z)$ is a polynomial of degree $n$ having all its zeros on $|z| = k$, $k \leq 1$, then it is proved[5] that $$\max_{|z|=1}|p′(z)| \leq\frac{n}{k^{n−1}+k^n}\max_{|z|=1}|p(z)|.$$In this paper, we generalize the above inequality by extending it to the polar derivative of a polynomial of the type $p(z) = c_nz^n +\sum\limits_{j=\mu}^{n}c_{n-j}z^{n-j}$, $1 \leq \mu \leq n$. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros.
}, issn = {1573-8175}, doi = {https://doi.org/10.1007/s10496-011-0150-3}, url = {http://global-sci.org/intro/article_detail/ata/4588.html} }If $p(z)$ is a polynomial of degree $n$ having all its zeros on $|z| = k$, $k \leq 1$, then it is proved[5] that $$\max_{|z|=1}|p′(z)| \leq\frac{n}{k^{n−1}+k^n}\max_{|z|=1}|p(z)|.$$In this paper, we generalize the above inequality by extending it to the polar derivative of a polynomial of the type $p(z) = c_nz^n +\sum\limits_{j=\mu}^{n}c_{n-j}z^{n-j}$, $1 \leq \mu \leq n$. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros.