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Zygmund’s Type Inequality to the Polar Derivative of a Polynomial

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Abstract:

In this paper we improve a result recently proved by Irshad et al. [On the Inequalities Concerning to the Polar Derivative of a Polynomial with Restricted Zeroes, Thai Journal of Mathematics, 2014 (Article in Press)] and also extend Zygmund's inequality to the polar derivative of a polynomial.

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Periodical:
International Journal of Advanced Research in Mathematics (Volume 5)
Pages:
52-59
Citation:
M.S. Pukhta "Zygmund’s Type Inequality to the Polar Derivative of a Polynomial", International Journal of Advanced Research in Mathematics, Vol. 5, pp. 52-59, 2016
Online since:
June 2016
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References:

[1] S. Bernstein, Lecons sur Less propries extréxtremaleset la meilleure dune fonctions, (Paris, 1926).

[2] A. Zygmund, A remark on conjugate series, Proc. London Math. Soc. 34(2) (1932), 392-400.

[3] A. Aziz and W.M. Shah, Inequalities for the polar derivaive of a polynomial, Indian J. Pure Appl. Math., 29 (1998), 163-173.

[4] A. Aziz and N.A. Rather, Some Zygmunds type Lp-inequlaity for polynomial, J. Math. Anal. Appl., 289 (2004), 14-29.

[5] N.G. De-Bruijin, Inequalitis concerning polynomials in the complex domain, Nedrel. Akad. Weternsch. Proc. Ser. A., 50 (1947), 1265-1272; Indag. Math., 9 (1947), 591-598.

[6] A. Aziz and N.A. Rather, On an inequality concerning the polar derivative of a poly, Proc. Indian Acad. Sci. (Math. Sci. ), 117(3) (August 2003), 349-357.

[7] Irshad Ahmed, A. Liman and W.M. Shah, On the inequalities concering to the polar derivative of a polynomial with restricted zeros, Thai Journal of Mathematics, (2014).

[8] G. Singh, W.M. Shah and A. Liman, A generalized inequality for the polar deriviative of polynomial, Journal of Inequalities and Applicaitons, 2013 2013: 183.

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