Document Type : Research Paper


1 Faculty of Science and Arts, Department of Mathematics, Düzce University, Düzce, Turkey.

2 Faculty of Science and Arts, Department of Mathematics, Tekirdağ Namık Kemal University, Tekirdağ, Turkey.


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 $2^{-r}$.


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