Inequalities for Polynomials with a Prescribed Zero

Abstract

If P(z) is a polynomial of degree n, then the inequality1is trivial. It was asked by Callahan [1], what improvement results from supposing that P(z) has a zero on |z| = 1 and he answered the question by showing that if P( l ) = 0, then2Donaldson and Rahman [3] have shown that if P(z) is a polynomial of degree n such that P(β) = 0 where β is an arbitrary non-negative number, then3whereas if the polynomial P(z) is such that P(l) = 0, then [4]4