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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