Some Inequalities Concerning the Polar Derivative of a Polynomial

Abdullah Mir, Bilal Dar

Abstract


In this paper, we consider the class of polynomials$P(z)=a_{n}z^{n}+\sum\limits_{\nu=\mu}^{n}a_{n-\nu}z^{n-\nu}, 1\leq\mu\leq n$, having all zeros in $|z|\leq k,~k\leq 1$ and thereby establish several interesting estimates pertaining to the maximum modulus of the polar derivative of a polynomial $P(z)$. Our results not only generalize and refine some known polynomial inequalities, but also a variety of interesting results can be deduced from these by a fairly uniform procedure.

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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|