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Rate of growth of polynomials with restricted zeros


ABDULLAH MIR, Q. M. DAWOOD


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abs_cmi_2016_25_2_197-203

In this paper we consider for a fixed µ, the class of polynomials P(z) = a0 + Pn ν=µ aνzν, 1 ≤ µ ≤ n, of degree at most n not vanishing in the disk |z| < k, k > 0. For any ρ > σ ≥ 1 and 0 < r ≤ R ≤ k, we investigate the dependence of k P(ρz) − P(σz) kR on k P kr and derive various refinements and generalizations of some well known results.