Growth Theorems for a Subclass of Strongly Spirallike Functions

Abstract

In this paper we consider a subclass of strongly spirallike functions on the unit disk $D$ in the complex plane $\mathbb{C}$, namely, strongly almost spirallike functions of type $\beta$ and order $\alpha$. We obtain the growth results for strongly almost spirallike functions of type $\beta$ and order $\alpha$ on the unit disk $D$ in $\mathbb{C}$ by using subordination principles and the geometric properties of analytic mappings. Furthermore we get the growth theorems for strongly almost starlike functions of order $\alpha$ and strongly starlike functions on the unit disk $D$ of $\mathbb{C}$. These growth results follow the deviation results of these functions.