Some remarks on a paper of L. Tóth.

De Koninck, Jean-Marie; Kátai, Imre

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On the mean values of an analytic function.

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Annales Polonici Mathematici

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Let f(z), $z = r e^{i θ}$ , be analytic in the finite disc |z| < R. The growth properties of f(z) are studied using the mean values $I_{δ} (r)$ and the iterated mean values $N_{δ, k} (r)$ of f(z). A convexity result for the above mean values is obtained and their relative growth is studied using the order and type of f(z).