MMN-3625

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

• Hari Mohan Srivastava, Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada, harimsri@math.uvic.ca
• Abbas Kareem Wanas, Department of Mathematics, College of Science, University of Al-Qadisiyah, Al Diwaniyah, Al-Qadisiyah, Iraq, abbas.kareem.w@qu.edu.iq

## Abstract

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.

Vol. 23 (2022), No. 2, pp. 889-896
DOI: 10.18514/MMN.2022.3625