A note on the Erdös-Lax inequality concerning polynomials

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.