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