Pre-Schwarzian norm estimation for functions in the Ma-Minda-type starlike and convex classes

Abstract

In this paper, we establish the sharp estimates of the pre-Schwarzian norm of functions $f$ in the Ma-Minda type starlike and convex classes ${\mathcal{S}}^{\ast }(\phi )$ and $\mathcal{C}(\phi )$, respectively, whenever $\phi (z)=3/\left(3+(\alpha -3)z-\alpha z^2\right)$ with $-3<\alpha \le 1$, $\phi (z)=(1+z)(1-sz)$ with $-1/3\le s\le 1/3$ and $\phi (z)=1+z/\left((1-z)(1+\alpha z)\right)$ with $0\le \alpha \le 1/2$.

18 Pages, Latex v1. arXiv admin note: substantial text overlap with arXiv:2504.19132