| 关于某类解析函数的星象性和Ruscheweyh的一个问题 |
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| 引用本文： | 刘名生. 关于某类解析函数的星象性和Ruscheweyh的一个问题[J]. 数学进展, 2005, 34(4): 416-424 |
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| 作者姓名： | 刘名生 |
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| 作者单位： | 华南师范大学数学系,广州,广东,510631,中国 |
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| 基金项目： | This research is supported by the National Natural Science Foundation of China（No. 10471048）. |
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| 摘 要： | 本文引入了一个涉及Ruscheweyh导数的解析函数子类，应用微分从属方法和Carlson-Shaffer算子讨论了它的从属关系和偏差定理；其次，应用单叶函数的性质和一个微分不等式研究了它的星象性条件和覆盖定理，最后，部分地解决了Ruscheweyh的一个问题。
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| 关 键 词： | 从属 星象函数 偏差定理 覆盖定理 |
| 文章编号： | 1000-0917（2005）04-0416-09 |
| 收稿时间： | 2003-03-24 |
| 修稿时间： | 2003-03-24 |
On the Starlikeness for Certain Subclass of Analytic Functions and a Problem of Ruscheweyh |
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| LIU Ming-sheng. On the Starlikeness for Certain Subclass of Analytic Functions and a Problem of Ruscheweyh[J]. Advances in Mathematics(China), 2005, 34(4): 416-424 |
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| Authors: | LIU Ming-sheng |
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| Abstract: | In this paper, a subclass of analytic functions involving Ruscheweyh derivatives is introduced. We discusse its subordinate relations and distortion theorems by using differential subordinate method and Carlson-Shaffer operator. Next, we study its condition of starlikeness and covering theorems by using the properties of univalent functions and a differential inequality. Finally, we give a part of answer to a problem of Ruscheweyh. |
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| Keywords: | subordination starlike function distortion theorem covering theorem |
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