Estimation of derivatives for regular positive real part functions

Abstract

In this paper, we mainly discuss the problem of estimating the $n$th derivative of regular positive real part functions: $ g(z)=c_0+c_1z+\cdots+c_nz^n+\cdots $, which is regular in $ |z|<1 $ and $ \Re g(z)>0 $. With the principle of inductive method and the characters of regular positive real part functions, the estimation of the $n$th derivative for the function $ g(z) $ is presented. The derivative estimation for positive functions with real part has been solved completely.