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

Miskolc Mathematical Notes

article

Hari Mohan Srivastava¹  Abbas Kareem Wanas² 

[1] Department of Mathematics and Statistics, University of Victoria;Department of Mathematics, College of Science, University of Al-Qadisiyah

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

DOI  :  10.18514/MMN.2022.3625

学科分类：数学（综合）

来源: Miskolci Egyetem

【 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.

【 授权许可】

CC BY