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Some Results on the Polar Derivative of a Polynomial

Some Results on the Polar Derivative of a Polynomial
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摘要 Let P(z) be a polynomial of degree n and for any complex number α, let DαP(z) = nP(z)+ (α-z)P' (z) denote the polar derivative of P(z) with respect to α. In this paper, we obtain certain inequalities for the polar derivative of a polynomial with restricted zeros. Our results generalize and sharpen some well-known polynomial inequalities. Let P(z) be a polynomial of degree n and for any complex number α, let DαP(z) = nP(z)+ (α-z)P' (z) denote the polar derivative of P(z) with respect to α. In this paper, we obtain certain inequalities for the polar derivative of a polynomial with restricted zeros. Our results generalize and sharpen some well-known polynomial inequalities.
出处 《Analysis in Theory and Applications》 2014年第3期306-317,共12页 分析理论与应用(英文刊)
关键词 POLYNOMIAL ZEROS polar derivative Bemstein inequality. Polynomial, zeros, polar derivative, Bemstein inequality.
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  • 1A. Aziz and W. M. Shah, An integral mean estimate for polynomial, Indian J. Pure Appl. Math., 28 (1997), 1413-1419.
  • 2S. Bernstein, Lecons sur les Proprietes Extremals et la Meilleure Approximation des Fonctions Analytiques d'une Fonctions Reelle, Cauthier-Villarsm, Paris, 1926.
  • 3K. K. Dewan, Narish Singh and Abdullah Mir, Extensions of some polynomial inequalities to the polar derivative, J. Math. Anal. Appl., 352 (2009), 807-815.
  • 4K. K. Dewan, Narish Singh and Roshan Lal, Inequalities for the polar derivative of a polynomial, Int. J. Pure Appl. Math., 33 (2006), 109-117.
  • 5N. K. Covil, Some inequalities for derivatives of polynomials, J. Approx. Theory, 66 (1991), 29-35.
  • 6M. A. Malik, On the derivative of a polynomial, J. London Math. Soc., 1 (1969),57-60.
  • 7P. Turan, Uber die ableitung von polynomen, Compos. Math., 7 (1939), 89-95.
  • 8Abdul Aziz,Nisar Ahmad Rather.New integral mean estimates for polynomials[J].Proceedings of the Indian Academy of Sciences - Mathematical Sciences.1999(1)
  • 9R. P. Boas,Q. I. Rahman.Lp inequalities for polynomials and entire functions[J].Archive for Rational Mechanics and Analysis.1962(1)
  • 10Marcel Riesz.über Einen Sat’z des Herrn Serge Bernstein[J].Acta Mathematica.1916(1)

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