On some operator preserving inequalities between polynomials

Abstract

In this paper, some generalizations of lower bound estimates for the maximum modulus of the [Formula: see text]th polar derivative [Formula: see text], where [Formula: see text], [Formula: see text] of polynomials are established under the assumption that one of the underlying polynomials [Formula: see text] and [Formula: see text] does not vanish in [Formula: see text]. The obtained estimates include several known lower bounds for polar derivatives as special cases.