This paper is mainly about holomorphic mappings associated with conic regions which are closely connected with k — ST(α). We introduce new subclasses of starlike (spirallike) functions, namely, S ^p_c (k,α)(S ^p_c (k,α,β)), and discuss their coefficient estimates and the Fekete-Szegö-Goluzin’s problem. Then we generalize S ^p_c (k,α,β) on the unit ball Bⁿ in ℂⁿ, that is, k-conic spirallike mappings of type β and order α. We obtain the growth, covering and distortion theorems of the generalized mappings. Besides that, we construct k-conic spirallike mappings of type β and order α on Bⁿ through S_c(k,α,β) by the generalized Roper-Suffridge extension operators.

本文主要是关于与它们紧密相连的圆锥区域相关联的全纯映射ķ - ST（α）。我们介绍了星形（螺旋状）函数的新子类，即S ^p _c（k，α）（S ^p _c（k，α，β）），并讨论了它们的系数估计和Fekete-Szegö-Goluzin问题。然后，我们概括小号^p _Ç（K，α，β）上的单位球乙^ñ在ℂ ^Ñ，即，ķ类型的-conic螺旋映照β和顺序α 。我们获得了广义映射的增长，覆盖和变形定理。除此之外，我们利用广义的Roper-Suffridge扩展算子在B ⁿ到S _c（k，α，β）上构造了β型和阶α的k型锥螺旋状映射。