ESTIMATES FOR A CERTAIN SUBCLASS OF HOLOMORPHIC FUNCTIONS

Abstract

In this paper, a version of the boundary Schwarz Lemma for the holomorphic function belonging to N(alpha) is investigated. For the function f(z) = z + c(2)z(2) + c(3)z(3) + ... which is defined in the unit disc where f(z) is an element of N(alpha), we estimate the modulus of the angular derivative of the function f(z) at the boundary point b with f (b) = 1/b integral(b)(0) f(t)dt. The sharpness of these inequalities is also proved.