| Salagean算子定义的双单叶函数子类的系数估计 |
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| 引用本文： | 陈帆,李晓飞.Salagean算子定义的双单叶函数子类的系数估计[J].数学研究及应用,2017,37(3):280-298. |
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| 作者姓名： | 陈帆 李晓飞 |
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| 作者单位： | 长江大学工程技术学院, 湖北 荆州 434000,长江大学信息与数学学院, 湖北 荆州 434000; 澳门大学数学系, 中国 澳门 999078 |
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| 基金项目： | 国家自然科学基金(Grant No.11401186),长江大学工程技术学院科技创新基金资助(Grant No.15J0802). |
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| 摘 要： | In this paper, a new subclass N_Σ~(h,p)(m, λ, μ) of analytic and bi-univalent functions in the open unit disk U is defined by salagean operator. We obtain coefficients bounds |a_2| and |a_3| for functions of the class. Moreover, we verify Brannan and Clunie's conjecture |a_2| ≤2~(1/2)for some of our classes. The results in this paper extend many results recently researched by many authors.
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| 关 键 词： | 解析函数 单叶函数 双单叶函数 系数估计 Salagean算子 |
| 收稿时间： | 2016/7/29 0:00:00 |
| 修稿时间： | 2016/9/7 0:00:00 |
Coefficient Bounds for a New Subclass of Bi-Univalent Functions Defined by Salagean Operator |
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| Fan CHEN and Xiaofei LI.Coefficient Bounds for a New Subclass of Bi-Univalent Functions Defined by Salagean Operator[J].Journal of Mathematical Research with Applications,2017,37(3):280-298. |
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| Authors: | Fan CHEN and Xiaofei LI |
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| Institution: | College of Engineering and Technology, Yangtze University, Hubei 434000, P. R. China and School of Information and Mathematics, Yangtze University, Hubei $434000$, P. R. China; Department of Mathematics, University of Macau, Macau 999078, P. R. China |
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| Abstract: | In this paper, a new subclass $\mathcal {N}^{h,p}_{\Sigma}(m,\lambda,\mu)$ of analytic and bi-univalent functions in the open unit disk $\mathbb{U}$ is defined by salagean operator. We obtain coefficients bounds $|a_{2}|$ and $|a_{3}|$ for functions of the class. Moreover, we verify Brannan and Clunie''s conjecture $|a_{2}|\leq\sqrt{2}$ for some of our classes. The results in this paper extend many results recently researched by many authors. |
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| Keywords: | analytic functions univalent functions bi-univalent functions coefficient bounds Salagean operator |
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