SOME RESULTS OF THE CARATHEODORY'S INEQUALITY AT THE BOUNDARY

Abstract

In this paper, a boundary version of the Caratheodory's inequality is investigated. We shall give an estimate below vertical bar f' (b)vertical bar according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and z(1) not equal 0. The sharpness of these estimates is also proved.