有界正则函数的导数估计

ESTIMATION OF DERIVATIVES FOR BOUNDED REGULAR FUNCTIONS

在这篇文章中 ,主要讨论了 n阶导数的估计式 ,即对有界正则函数 φ(z) =c0 +c1z+… +cnzn+… (在 |z|<1内正则 ) ,从已知的三阶、四阶导数估计式 ,利用归纳法原理及有界正则函数的性质推出 n阶导数的一般估计式 ,并推出在 |z|<1内正则的正实部函数的 n阶导数的一般估计式 .

In this paper, we mainly discuss the problem of estimating the n-th derivative of bounded function: φ(z)=c 0+c 1z+...+c nz n+..., which is regular under the condition|z|<1. From the known estimation of the 3 rd and 4-th derivative, a generalized estimation of the n-th derivative of the function is presented by using the principle of the inductive method and the characters of the bounded regular function. Then a similar result of the special regular function, its real part is positive in the scope of|z|<1, is given.