On the mean values of an analytic function.

Let f(z), ${\displaystyle z=r{e}^{i\theta }}$, be analytic in the finite disc |z| < R. The growth properties of f(z) are studied using the mean values ${\displaystyle I_{\delta }\left(r\right)}$ and the iterated mean values ${\displaystyle N_{\delta ,k}\left(r\right)}$ 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).