Some applications of first-order differential subordinations for holomorphic functions in complex normed spaces

[摘要] In Geometric Function Theory of Complex Analysis, there have been many interesting and fruitful usages of a wide variety of differential subordinations for holomorphic functions in the unit disk $\mathbb{U}$: $$\mathbb{U}=\left\lbrace z: z\in \mathbb{C} \quad \text{and} \quad |z|<1 \right\rbrace.$$ Here, in this article, we derive some properties of the first-order differential subordinations for holomorphic functions which are defined in the unit ball $\mathbb{B}$: $$\mathbb{B}=\left\lbrace z: z\in \mathbb{C}^{n} \quad \text{and} \quad \|z\|<1 \right\rbrace$$ by using a certain class of admissible functions. We also make use of the theory of biholomprphic functions in our investigation here.

[学科分类] 数学（综合）

[关键词] holomorphic functions;differential subordinations;admissible functions;normed spaces;biholomorphic functions;unit disk;unit ball