The purpose of this note is to give, first, a general formulation of the extremal func- tion withiıı the class E of analytic functions that can be represented by means of a Stieltjes integral such as considered by Goluzin and then to apply the result in a systematic way, say, to analytic functions with positive real part. We also called attention to söme errors in Goluzin’s paper (translated by A. W. Goodman).