Research Article
BibTex RIS Cite

Year 2016, Volume: 4 Issue: 2, 110 - 120, 30.10.2016

Abdullah Mir

https://doi.org/10.36753/mathenot.421464
Cited By: 1

Abstract

References

  • [1] A. Mir and B. Dar., Some inequalities concerning the polar derivative of a polynomial-II, Anal. Theory Appl., 29 (2013), 384-389.
  • [2] A. Aziz and Q. M. Dawood., Inequalities for a polynomial and its derivative, J. Approx. Theory, 54 (1988), 306-313.
  • [3] A. Aziz and N. A. Rather., Some Zygmund type Lq−inequalities for polynomials, J. Math. Anal. Appl., 289 (2004), 14-29.
  • [4] A.Aziz and N.A.Rather., Inequalities for the polar derivative of a polynomial with restricted zeros, Math. Balk., 17 (2003), 15-28.
  • [5] A. Aziz and N. A. Rather., A refinement of a theorem of Paul Turan concerning polynomials, Math. Ineq. Appl., 1(1998), 231-238.
  • [6] A. Aziz and W. M. Shah., An integral mean estimate for polynomials, Indian J. Pure Appl. Math., 28 (1997), 1413-1419.
  • [7] S. Bernstein., Lecons Sur Les Proprietes extremals et la meilleure approximation des fonctions analytiques d’une fonctions reelle, Gauthier-villars (Paris 1926).
  • [8] K. K. Dewan, N. Singh and R. Lal., Inequalities for the polar derivative of a polynomial, Int. J. Pure. Appl. Math., 33 (2006), 109-117.
  • [9] K. K. Dewan, N. Singh and A. Mir., Extensions of some polynomial inequalities to the polar derivative, J. Math. Anal. Appl., 352 (2009), 807-815.
  • [10] K. K. Dewan, A. Mir and R. S. Yadav., Integral mean estimates for polynomials whose zeros are with in a circle, IJMMS, 4 (2001), 231-235.
  • [11] K. K. Dewan, N. Singh, A. Mir and A. Bhat., Some inequalities for the polar derivative of a polynomial, Southeast Asain Bull. Math., 34 (2010), 69-77.
  • [12] N. K. Govil., Some inequalities for derivative of polynomials, J.Approx. Theory, 66 (1991), 29-35.
  • [13] N. K. Govil, Q. I. Rahman and G. Schemeisser., On the derivative of a polynomial, Illinois J. Math., 23 (1979), 319-330.
  • [14] E. Hille, Ananlytic function theory, Vol II, Ginn and Company, New York, Toranto, 1962.
  • [15] M. A. Malik., On the derivative of a polynomial, J. London Math. Soc., 1 (1969), 57-60.
  • [16] M. Riesz., Eine trigonometrische interpolationsformel und einige Ungleichungen für Polynome, Jahresbericht der Deutschen Mathematiker-Vereinigung, 23 (1914), 354-368.
  • [17] P. Turán., Über die ableitung von polynomen, Compositio Math., 7 (1939), 89-95.

On Polynomials and Their Polar Derivative

Year 2016, Volume: 4 Issue: 2, 110 - 120, 30.10.2016

Abdullah Mir

https://doi.org/10.36753/mathenot.421464
Cited By: 1

Abstract


Keywords

Polar derivative polynomials zeros L^γ−inequalities in the complex domain

References

  • [1] A. Mir and B. Dar., Some inequalities concerning the polar derivative of a polynomial-II, Anal. Theory Appl., 29 (2013), 384-389.
  • [2] A. Aziz and Q. M. Dawood., Inequalities for a polynomial and its derivative, J. Approx. Theory, 54 (1988), 306-313.
  • [3] A. Aziz and N. A. Rather., Some Zygmund type Lq−inequalities for polynomials, J. Math. Anal. Appl., 289 (2004), 14-29.
  • [4] A.Aziz and N.A.Rather., Inequalities for the polar derivative of a polynomial with restricted zeros, Math. Balk., 17 (2003), 15-28.
  • [5] A. Aziz and N. A. Rather., A refinement of a theorem of Paul Turan concerning polynomials, Math. Ineq. Appl., 1(1998), 231-238.
  • [6] A. Aziz and W. M. Shah., An integral mean estimate for polynomials, Indian J. Pure Appl. Math., 28 (1997), 1413-1419.
  • [7] S. Bernstein., Lecons Sur Les Proprietes extremals et la meilleure approximation des fonctions analytiques d’une fonctions reelle, Gauthier-villars (Paris 1926).
  • [8] K. K. Dewan, N. Singh and R. Lal., Inequalities for the polar derivative of a polynomial, Int. J. Pure. Appl. Math., 33 (2006), 109-117.
  • [9] K. K. Dewan, N. Singh and A. Mir., Extensions of some polynomial inequalities to the polar derivative, J. Math. Anal. Appl., 352 (2009), 807-815.
  • [10] K. K. Dewan, A. Mir and R. S. Yadav., Integral mean estimates for polynomials whose zeros are with in a circle, IJMMS, 4 (2001), 231-235.
  • [11] K. K. Dewan, N. Singh, A. Mir and A. Bhat., Some inequalities for the polar derivative of a polynomial, Southeast Asain Bull. Math., 34 (2010), 69-77.
  • [12] N. K. Govil., Some inequalities for derivative of polynomials, J.Approx. Theory, 66 (1991), 29-35.
  • [13] N. K. Govil, Q. I. Rahman and G. Schemeisser., On the derivative of a polynomial, Illinois J. Math., 23 (1979), 319-330.
  • [14] E. Hille, Ananlytic function theory, Vol II, Ginn and Company, New York, Toranto, 1962.
  • [15] M. A. Malik., On the derivative of a polynomial, J. London Math. Soc., 1 (1969), 57-60.
  • [16] M. Riesz., Eine trigonometrische interpolationsformel und einige Ungleichungen für Polynome, Jahresbericht der Deutschen Mathematiker-Vereinigung, 23 (1914), 354-368.
  • [17] P. Turán., Über die ableitung von polynomen, Compositio Math., 7 (1939), 89-95.
There are 17 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Abdullah Mir

Publication Date October 30, 2016
Submission Date September 4, 2015
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

APA Mir, A. (2016). On Polynomials and Their Polar Derivative. Mathematical Sciences and Applications E-Notes, 4(2), 110-120. https://doi.org/10.36753/mathenot.421464
AMA Mir A. On Polynomials and Their Polar Derivative. Math. Sci. Appl. E-Notes. October 2016;4(2):110-120. doi:10.36753/mathenot.421464
Chicago Mir, Abdullah. “On Polynomials and Their Polar Derivative”. Mathematical Sciences and Applications E-Notes 4, no. 2 (October 2016): 110-20. https://doi.org/10.36753/mathenot.421464.
EndNote Mir A (October 1, 2016) On Polynomials and Their Polar Derivative. Mathematical Sciences and Applications E-Notes 4 2 110–120.
IEEE A. Mir, “On Polynomials and Their Polar Derivative”, Math. Sci. Appl. E-Notes, vol. 4, no. 2, pp. 110–120, 2016, doi: 10.36753/mathenot.421464.
ISNAD Mir, Abdullah. “On Polynomials and Their Polar Derivative”. Mathematical Sciences and Applications E-Notes 4/2 (October 2016), 110-120. https://doi.org/10.36753/mathenot.421464.
JAMA Mir A. On Polynomials and Their Polar Derivative. Math. Sci. Appl. E-Notes. 2016;4:110–120.
MLA Mir, Abdullah. “On Polynomials and Their Polar Derivative”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 2, 2016, pp. 110-2, doi:10.36753/mathenot.421464.
Vancouver Mir A. On Polynomials and Their Polar Derivative. Math. Sci. Appl. E-Notes. 2016;4(2):110-2.

Cited By

Lγ Inequalities for the Polar Derivative of Polynomials
Malaysian Journal of Mathematical Sciences
https://doi.org/10.47836/mjms.17.3.06

20477

The published articles in MSAEN are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.