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).

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