Pre-Schwarzian Norm Estimates for the class of Janowski Starlike Functions

Abstract

For $-1\le B<A\le 1$, let ${\mathcal{S}}^{\ast }(A,B)$ denote the class of Janowski starlike functions which satisfy the subordination relation $z{f}^{\prime }(z)/f(z)\prec (1+Az)/(1+Bz)$. In the present article, we determine the sharp of pre-Schwarzian norm for the functions in the class ${\mathcal{S}}^{\ast }(A,B)$.

arXiv comment13 pages