| 调和单叶函数族的一些结果 |
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| 引用本文： | 熊良鹏,王雅倩.调和单叶函数族的一些结果[J].数学研究及应用,2022,42(5):499-510. |
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| 作者姓名： | 熊良鹏 王雅倩 |
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| 作者单位： | 江西科技师范大学数学与计算机科学学院, 江西 南昌 330038 |
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| 基金项目： | 国家自然科学基金(Grant No.12061035),江西省自然科学基金(Grant No.20212BAB201012),江西省教育厅科研项目(Grant No.GJJ201104),江西科技师范大学青年拔尖人才项目(Grant No.2021QNBJRC003). |
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| 摘 要： | 借用著名的Ruscheweyh导数,引入了一类单叶保向调和函数族. 通过建立极值理论,得到了关联该族的最优系数边界、最优增长定理和最优偏差定理. 同时,给出了该族与先前已有调和函数族之间的转换半径. 最后,讨论了基于该族的修正哈达玛乘积结果.
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| 关 键 词： | 极值点 增长定理 调和函数 修正哈达玛乘积 Ruscheweyh导数 |
| 收稿时间： | 2021/8/15 0:00:00 |
| 修稿时间： | 2022/2/19 0:00:00 |
Some Results for a Family of Harmonic Univalent Functions |
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| Xiangpeng XIONG,Yaqian WANG.Some Results for a Family of Harmonic Univalent Functions[J].Journal of Mathematical Research with Applications,2022,42(5):499-510. |
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| Authors: | Xiangpeng XIONG Yaqian WANG |
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| Affiliation: | School of Mathematics and Computer Science, Jiangxi Science and Technology Normal University, Jiangxi 330038, P. R. China |
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| Abstract: | In this paper, we introduce a class of the univalent sense-preserving harmonic functions associated with Ruscheweyh derivatives. By establishing the extremal theory, we obtain the sharp coefficients bounds, sharp growth theorems and sharp distortion theorems for the class. The radius equation between this class and a known class of harmonic functions is given. Also, we investigate the results of modified-Hadamard product for this class. |
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| Keywords: | extreme points growth theorem harmonic functions modified-Hadamard product Ruscheweyh derivatives |
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