Abstract. Suppose that $G\subset C $ is a Jordan domain and let the functions $f_n$ be holomorphic on $\overline{G}$. Assume that $U$ is a neighborhood of a point $z_0 \in\partial G$. In this paper the ``size'' of $f_n (U)$ is estimated. As application of the main result, informations about the boundary behavior of the partial sums, Ces?ro and Riesz means of power series are obtained.

DOI: 10.14232/actasm-013-084-7

AMS Subject Classification (1991): 30B10, 30C15

Keyword(s): boundary behavior, distribution of values, Jentzsch-type theorems

Received December 13, 2013, and in final form August 12, 2014. (Registered under 84/2013.)