Sharpened Forms for ?-Spirallike Function of Complex Order on the Boundary

Abstract

We present a different version of Schwarz Lemma and estimate the angular derivative of the function zf'(z)/f(z) from below for lambda-spirallike function f(z) of complex order at the boundary of the unit disc D by taking into account of the zeros of the function f(z) - z which are different from zero.