General Univalence Criterion Associated with the nth Derivative

Abstract

For normalized analytic functions $f\left(z\right)$ with $f\left(z\right)\ne 0$ for , we introduce a univalencecriterion defined by sharp inequality associated with the $n$th derivative of $z/f\left(z\right)$, where $n\in \left\{\mathrm{3,4},5,\dots \right\}$.