论文标题
关于$ n $ - 对称，结合和对称共轭点
On functions starlike with respect to $n$-ply symmetric, conjugate and symmetric conjugate points
论文作者
论文摘要
对于给定的非负实数，$ \ sum_ {k = 1}^{m}α_k= 1 $和归一化的分析函数$ f_k $，$ k = 1，\ dotsc，m $，定义在开放的单位光盘上，让$ f $ f $ f $ f $ f $ f_n $定义f（z）：= \ sum_ {k = 1}^{m}α_kf_k（z）$和$ f_ {n}（z）：= n^{ - 1} \ sum_ {j = 0}^{n-1}^{n-1}本文研究了满足从属的功能$ f_k $ $ zf'_ {k}（z）/f_ {n}（z）（z）\ prec h（z）$，其中函数$ h $是凸的单价函数，具有正面实际部分。我们还考虑了相对于对称，结合和对称共轭点的类似星状函数的类似物。这些和相关类别证明了包容性和卷积结果。我们的课程概括了几个众所周知的课程，并指出了与以前的作品的联系。
For given non-negative real numbers $α_k$ with $ \sum_{k=1}^{m}α_k =1$ and normalized analytic functions $f_k$, $k=1,\dotsc,m$, defined on the open unit disc, let the functions $F$ and $F_n$ be defined by $ F(z):=\sum_{k=1}^{m}α_k f_k (z)$, and $F_{n}(z):=n^{-1}\sum_{j=0}^{n-1} e^{-2jπi/n} F(e^{2jπi/n} z)$. This paper studies the functions $f_k$ satisfying the subordination $zf'_{k} (z)/F_{n} (z) \prec h(z)$ where the function $h$ is a convex univalent function with positive real part. We also consider the analogues of the classes of starlike functions with respect to symmetric, conjugate, and symmetric conjugate points. Inclusion and convolution results are proved for these and related classes. Our classes generalize several well-known classes and connection with the previous works are indicated.
