Abstract

In this paper, a version of the boundary Schwarz Lemma for the holomorphic function belonging to <TEX>$\mathcal{N}$</TEX>(<TEX>${\alpha}$</TEX>) is investigated. For the function <TEX>$f(z)=z+c_2z^2+C_3z^3+{\cdots}$</TEX> which is defined in the unit disc where <TEX>$f(z){\in}\mathcal{N}({\alpha})$</TEX>, we estimate the modulus of the angular derivative of the function f(z) at the boundary point b with <TEX>$f(b)={\frac{1}{b}}\int\limits_0^b$</TEX> f(t)dt. The sharpness of these inequalities is also proved.