A note on the Erdös-Lax inequality concerning polynomials. (English) Zbl 1521.30013
Summary: 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.
MSC:
| 30C10 | Polynomials and rational functions of one complex variable |
| 30D15 | Special classes of entire functions of one complex variable and growth estimates |
| 30A10 | Inequalities in the complex plane |
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