| 熊良鹏.Janowski星形和凸函数族相关的非线性积分算子性质[J].数学研究及应用,2016,36(4):432~440 |
| Janowski星形和凸函数族相关的非线性积分算子性质 |
| Properties of Certain Nonlinear Integral Operator Associated with Janowski Starlike and Convex Functions |
| 投稿时间：2015-08-22 修订日期：2016-01-13 |
| DOI：10.3770/j.issn:2095-2651.2016.04.005 |
| 中文关键词: 解析函数 Janowski 函数 非线性积分算子 有界边界旋转函数 从属 |
| 英文关键词:analytic functions Janowski functions nonlinear integral operators functions with bounded boundary rotation subordination |
| 基金项目:四川省教育厅科研项目资助 (Grant No.14ZB0364). |
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| 中文摘要: |
| 考虑了一般化非线性积分算子$\mathscr{H}_{\alpha_i,\beta_i}(f_1,\ldots,f_n;g_1,\ldots,g_n)(z)$,得到该算子关于系数估计、单叶性条件和凸性半径的一些结果. 进一步推导了介于$\mathscr{H}_{\alpha_i,\beta_i}(f_1,\ldots,f_n;g_1,\ldots,g_n)(z)$和一些有界边界旋转解析函数子类之间的映射性质.通过给定特殊参数,许多其他相关族的类似结果可以间接给出. |
| 英文摘要: |
| In this paper, we consider a general nonlinear integral operator $\mathscr{H}_{\alpha_i,\beta_i}(f_1,\ldots,f_n$; $g_1,\ldots,g_n)(z)$. Some results including coefficient problems, univalency condition and radius of convexity for this integral operator are given. Furthermore, we discuss the mapping properties between $\mathscr{H}_{\alpha_i,\beta_i}(f_1,\ldots,f_n;g_1,\ldots,g_n)(z)$ and subclasses of analytic functions with bounded boundary rotation. The same subjects for some corresponding classes are shown upon specializing the parameters in our main results. |
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