A note on the Erdös-Lax inequality concerning polynomials

Abdullah Mir () and Tahir Fayaz ()
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Abdullah Mir: University of Kashmir
Tahir Fayaz: University of Kashmir

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 3, 936-945

Abstract: 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.

Keywords: Bernstein-type inequalities; Erdös-Lax inequality; Polar derivative of a polynomial; s-fold zeros; 30A10; 30C10; 30D15 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00309-7

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