International Journal of Nonlinear Analysis and Applications
On certain properties for new subclass of meromorphic starlike functions
Document Type : Research Paper
Authors
1 Department of Mathematics, Faculty of science, Lorestan University, 68151-4-4316, Khorramabad, Iran
2 Department of Mathematics, Faculty of science, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran
Abstract
In this paper we studying some properties of starlike function of order $\lambda$ which satisfy in the condition
$$\Re(\frac{zf^{'}(z)}{f(z)}+\alpha\frac{z^{2}f^{''}(z)}{f(z)})<1-\lambda+\alpha$$
\\for all $z\in U=\{z:|z|<1\}$, where $f(z)=1+\sum_{k=1}^\infty a_{k}z^{k}$ is analytic in $U$, $0\leqslant\alpha<2$ and $0\leqslant\lambda<1$. Our results extend previos results given by Aghalary et al. (2009) and Wang et al.(2014).
Keywords
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