Some integral mean estimates for polynomials

Abstract

In this paper, we establish some integral mean estimates for polynomials P (z) = a n z n + n υ=μ a n−υ z n−υ , 1 ≤ μ ≤ n, having all its zeros in |z| ≤ k, k ≤ 1. Our results not only generalize and refine some known polynomial inequalities, but also a variety of interesting results can be deduced from these by a fairly uniform procedure.