Convex and Starlike Functions Defined on the Subclass of the Class of the Univalent Functions $S$ with Order $2^{-r}$

Abstract

In this paper, some conditions have been improved so that the function $g(z)$ is defined as $g(z)=1+\sum_{k\ge 2}^{\infty}a_{n+k}z^{n+k}$, which is analytic in unit disk $U$, can be in more specific subclasses of the $S$ class, which is the most fundamental type of univalent function. It is analyzed some characteristics of starlike and convex functions of order $2^{-r}$.

Keywords

• analytic function
• convex function
• starlike function
• univalent function