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Some lower bounds for the derivative of certain polynomials

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Abstract

For the class of polynomials having no zero outside the disc \(\{z:|z| \le k \},\) there is considerable amount of literature concerning the estimation of lower bound of maximum of \(|P^{\prime }(z)|\) in terms of maximum of |P(z)|. However no such results are available when the polynomials have some zeros outside the disc \(\{z:|z| \le k \}\). In this paper we propose to obtain some estimates for the lower bound of maximum modulus of the derivative of a polynomial in terms of maximum modulus of the polynomial when some zeros of the polynomial lie outside the disc \(\{z:|z| \le k \}\).

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Acknowledgements

We are thankful to Professor N. A. Rather for kindly looking at the manuscript and giving some very useful suggestions. Also, we are grateful to the referees for their valuable suggestions, which have certainly enhanced the presentation of this paper

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Correspondence to Ishfaq Dar.

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Dar, I., Iqbal, A. Some lower bounds for the derivative of certain polynomials. Ann Univ Ferrara 66, 295–300 (2020). https://doi.org/10.1007/s11565-020-00344-4

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  • DOI: https://doi.org/10.1007/s11565-020-00344-4

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