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A note on the Erdös-Lax inequality concerning polynomials

Author

Listed:
  • Abdullah Mir

    (University of Kashmir)

  • Tahir Fayaz

    (University of Kashmir)

Abstract

In this paper, we establish some generalizations of the upper bound estimates for the modulus of the derivative of a polynomial on the unit disk while accounting for the positioning of the zeros and extremal coefficients of the underlying polynomial. We shall also extend the obtained results to the polar derivative of a polynomial. The estimates obtained sharpen as well as generalize some recently proved Erdös-Lax type inequalities.

Suggested Citation

  • Abdullah Mir & Tahir Fayaz, 2023. "A note on the Erdös-Lax inequality concerning polynomials," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(3), pages 936-945, September.
    • Handle: RePEc:spr:indpam:v:54:y:2023:i:3:d:10.1007_s13226-022-00309-7
    DOI: 10.1007/s13226-022-00309-7
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    References listed on IDEAS

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    1. N. K. Govil & P. Kumar, 2017. "On Bernstein-Type Inequalities for the Polar Derivative of a Polynomial," Springer Optimization and Its Applications, in: Narendra Kumar Govil & Ram Mohapatra & Mohammed A. Qazi & Gerhard Schmeisser (ed.), Progress in Approximation Theory and Applicable Complex Analysis, pages 41-74, Springer.
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