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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 20 | Number 1 | Year 2015 | Article Id. IJMTT-V20P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V20P509

Some Inequalities for the Polar Derivative of a Polynomial


K.K. Dewan, C.M. Upadhye
Abstract

In this paper we establish p L inequalities for polar derivatives of polynomials not vanishing in | z | 1. Also we obtain inequalities for polar derivatives of polynomials satisfying. Our results generalize some well-known results in this direction.

Keywords
Inequalities, Polar Derivative, Polynomial.
References

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[5] N.K. Govil, G. Nyuydinkong and B. Tameru, Some p L inequalities for the polar derivative of a polynomial, J. Math. Anal. Appl., 254(2001), 618--626.
[6] N.K. Govil and D.H. Vetterlein, Inequalities for a class of polynomials satisfying ( ) (1/ ) n P z z P z , Complex Variables, 29(1996), 1--7.
[7] V.K. Jain, Inequalities for polynomials satisfying ( ) (1/ ) n P z z P z , II, J. Indian Math. Soc., 59(1993), 167--170.
[8] E. Laguarre, ``Oeuvres'', 1 Gauthier-villars, Paris, (1898).
[9] P.D. Lax, Proof of a conjecture of P. Erdos on the derivative of a polynomial, Bull. Amer. Math. Soc., 50(1944), 509--513.
[10] M. Marden, Geometry of the zeros of polynomials in a complex variable, Math. Surveys, No. 3, Amer. Math. Soc., Providence, R.I., 1949.
[11] G. Polya and G. Szego, Aufgaben and Lehratze ous der Analysis, Springer-Verlag, Berlin, 1925.

Citation :

K.K. Dewan, C.M. Upadhye, "Some Inequalities for the Polar Derivative of a Polynomial," International Journal of Mathematics Trends and Technology (IJMTT), vol. 20, no. 1, pp. 70-74, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V20P509

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