Integral mean estimates for polynomials whose zeros are within a circle

Abstract

Let P(z) be a polynomial of degree n having all its zeros in |z| <= K <= 1, then for each δ > 0, p > 1, q > 1 with [InlineEquation not available: see fulltext.], Aziz and Ahmad (Glas Mat Ser III 31:229-237, 1996) proved that

[Equation not available: see fulltext.]

In this paper, we extend the above inequality to the class of polynomials [InlineEquation not available: see fulltext.], 1 <= [mu] <= n, having all its zeros in |z| <= K <= 1, and obtain a generalization as well as refinement of the above result.

Mathematics Subject Classification (2000)

30A10, 30C10, 30C15[PUBLICATION ABSTRACT]