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

TL;DR

This paper determines the exact bounds of the pre-Schwarzian norm for Janowski starlike functions, a specific class of univalent functions characterized by a subordination condition.

Contribution

It provides the sharp pre-Schwarzian norm estimates for the class of Janowski starlike functions, extending the understanding of their geometric properties.

Findings

Sharp bounds for pre-Schwarzian norm are established.

Results apply to the class of Janowski starlike functions with parameters A and B.

The bounds are proven to be optimal.

Abstract

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