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

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

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.