Convex and Starlike Functions Defined on the Subclass of the Class of the Univalent Functions S with Order ۲^{-r}

In this paper, some conditions have been improved so that the function g(z) is defined as g(z)=۱+\sum_{k\ge ۲}^{\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 ۲^{-r}.

Keywords:

Analytic function , convex function , Starlike function , Univalent function