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Some inequalities concerning polar derivative of a polynomial. Addendum

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Abstract

Let P(z) be s polynomial of degree n having all its zeros in |z| ≤ k, k ≥ 1. In this paper, we shall generalize a result of Aziz and Rather [2] which in turn provides an improvement of a recent result of Dewan et al. [4]. Also a refinement of a result of Shah [10] for the polar derivative of a polynomial has been obtained by using the location of the zeros of P(z).

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References

  1. A. Aziz and N. Ahmad, Proc. Ind. Acad. Sci. (Math Sci.) 107(2), 189 (1997).

    MathSciNet  MATH  Google Scholar 

  2. A. Aziz and N. A. Rather, J. Math. Ineq. Appl. 1, 231 (1998).

    MathSciNet  MATH  Google Scholar 

  3. A. Bhat, Bernstein Type of Inequalities and on Location of Zeros of Polynomials (Ph. D. Thesis Submitted to J.M.I., New Delhi, 1995).

  4. K. K. Dewan, Naresh Singh, Abdullah Mir, and A. Bhat, Southeast Asian Bulletin of Mathematics 34, 69 (2010).

    MathSciNet  Google Scholar 

  5. C. Frappier, Q. I. Rahman, and St. Ruscheweyh, Trans. Amer. Math. Soc. 288, 69 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  6. R. B. Gardner and N. K. Govil, J. Math. Anal. Appl. 179, 208 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  7. N. K. Govil, Proc. Amer. Math. Soc. 41, 543 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  8. N. K. Govil, J. Approx. Theory 66, 29 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  9. M. A. Malik, J. London Math. Soc. 1, 57 (1969).

    Article  MathSciNet  MATH  Google Scholar 

  10. W. M. Shah, J. Ramanujan Math. Soc. 11, 67 (1996).

    MathSciNet  MATH  Google Scholar 

  11. H. Singh, On a Problem of the Chemist Mendeleev and Related Problems on Polynomials (Ph.D. Thesis Submitted to J.M.I., New Delhi, 2001).

  12. P. Turan, Compositio Math. 7, 89 (1939).

    MathSciNet  MATH  Google Scholar 

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Correspondence to Abdullah Mir.

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Submitted by F.G. Avkhadiev

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Mir, A., Baba, S.A. Some inequalities concerning polar derivative of a polynomial. Addendum. Lobachevskii J Math 32, 231–237 (2011). https://doi.org/10.1134/S1995080211030103

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  • DOI: https://doi.org/10.1134/S1995080211030103

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