Mohd Nazran Mohammed PAUZI,Maslina DARUS,Saibah SIREGAR.The Starlikeness of Analytic Functions of Koebe Type with Complex Order[J].数学研究及应用,2018,38(6):586~596
The Starlikeness of Analytic Functions of Koebe Type with Complex Order
The Starlikeness of Analytic Functions of Koebe Type with Complex Order
投稿时间:2018-03-21  修订日期:2018-09-01
DOI:10.3770/j.issn:2095-2651.2018.06.005
中文关键词:  analytic function  subordination  superordination  Koebe type
英文关键词:analytic function  subordination  superordination  Koebe type
基金项目:Supported by UKM (Grant No.GUP-2017-064).
作者单位
Mohd Nazran Mohammed PAUZI School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Selangor, DE, Bangi UKM, 43600, Malaysia 
Maslina DARUS School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Selangor, DE, Bangi UKM, 43600, Malaysia 
Saibah SIREGAR Faculty of Engineering and Life Sciences, Universiti Selangor, Selangor, DE, UNISEL, 45600, Malaysia 
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中文摘要:
      For $\alpha > 0$, $\lambda>0$ and $\beta,\eta \in \mathbb{R} $, we consider the $M(\alpha,\lambda)_{b}$ of normalized analytic $\alpha-\lambda$ convex functions defined in the open unit disc $\U$. In this paper we investigate the class $M(\alpha,\lambda,\beta,\eta)_b$, with $f_{b}:= \frac{z }{(1-z^{n})^{b}}$ being Koebe type. By making use of Jack's Lemma as well as several differential and other inequalities, the authors derive sufficient conditions for starlikeness of the class $M(\alpha,\lambda,\beta,\eta)_b$ of $n$-fold symmetric analytic functions of Koebe type. Relevant connections of the results presented here with those given in earlier works are also indicated.
英文摘要:
      For $\alpha > 0$, $\lambda>0$ and $\beta,\eta \in \mathbb{R} $, we consider the $M(\alpha,\lambda)_{b}$ of normalized analytic $\alpha-\lambda$ convex functions defined in the open unit disc $\U$. In this paper we investigate the class $M(\alpha,\lambda,\beta,\eta)_b$, with $f_{b}:= \frac{z }{(1-z^{n})^{b}}$ being Koebe type. By making use of Jack's Lemma as well as several differential and other inequalities, the authors derive sufficient conditions for starlikeness of the class $M(\alpha,\lambda,\beta,\eta)_b$ of $n$-fold symmetric analytic functions of Koebe type. Relevant connections of the results presented here with those given in earlier works are also indicated.
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