An estimation of the pre-Schwarzian norm for certain classes of analytic functions

Abstract

The primary objective of this paper is to establish the sharp estimates of the pre-Schwarzian norm for functions $f$ in the class ${\mathcal{S}}^{\ast }(\phi )$ and $\mathcal{C}(\phi )$ when $\phi (z)=1/(1-z{)}^s$ with $0<s\le 1$ and $\phi (z)=(1+sz{)}^2$ with $0<s\le 1/\sqrt{2}$, where ${\mathcal{S}}^{\ast }(\phi )$ and $\mathcal{C}(\phi )$ are the Ma-Minda type starlike and Ma-Minda type convex classes associated with $\phi$, respectively.

Latex V1, Pages-15

References in corpus (1)

• The Schwarzian norm estimates for Janowski convex functions