A note on Erdös-Lax type inequalities for polynomials

Abstract The goal of this paper is to establish some results for the polar derivative of a polynomial in the plane that are inspired by a classical result of Erdös-Lax that relates the sup-norm of the derivative on the unit circle to that of the polynomial itself (on the unit circle) by using extreme coefficients of the given polynomial. The obtained results may be useful in various applications that required the Erdös-Lax type inequalities. Moreover, a numerical example is presented, showing that in some situations, the bounds obtained by our results can be considerably sharper than the previous ones known in very rich literature on this subject. Mathematics Subject Classi cation: Primary 30A10 , 30C10, Secondary 30D15.