Document Type : Research Paper
Authors
- Ä°smet YÄ±ldÄ±z ^{1}
- Oya Mert ^{} ^{} ^{2}
- Alaattin Akyar ^{1}
^{1} Faculty of Science and Arts, Department of Mathematics, Düzce University, Düzce, Turkey.
^{2} Faculty of Science and Arts, Department of Mathematics, TekirdaÄŸ NamÄ±k Kemal University, TekirdaÄŸ, Turkey.
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
[2] A.W. Goodman, Univalent functions- Vols. I and II, Polygonal Pub., Washington, New Jersey, 1983.
[3] J. Li and S. Owa, Sufficient conditions for starlikeness, Indian J. Pure Appl. Math. 33(9) (2002), pp. 1385–1390.