The Landau-Bloch type theorems for certain class of holomorphic and pluriharmonic mappings in ${\mathbb{c}}^n$

In this paper, we first define two classes of holomorphic mappings defined on the unit ball $B^n$ of n-dimensional complex space ${\mathbb{C}}^n$ and obtain the lower estimates for Bloch’s constant for these classes. Also, we derive the Landau-Bloch type theorem for some subclasses of pluriharmonic mappings defined on the unit ball $B^n$.