A SHARP CARATHEODORY'S INEQUALITY ON THE BOUNDARY

Abstract

In this paper, a generalized boundary version of Caratheodory's inequality for holomorphic function satisfying f (z) <= f (0)+ a(p)z(p) + . . ., and Rf (z) = A for |z| < 1 is investigated. Also, we obtain sharp lower bounds on the angular derivative f '(c) at the point c with R f (c) = A. The sharpness of these estimates is also proved.