On Erdös–Lax and Turán-type inequalities for polynomials

Abstract

This paper considers the well-known Erdös–Lax and Turán-type inequalities that relate the sup-norm of a univariate complex coefficient polynomial and its derivative, when there is a restriction on its zeros. The obtained results produce inequalities that are sharper than the previous ones. Moreover, a numerical example is presented, showing that in some situations, the bounds obtained by our results can be considerably sharper than the ones previously known.