On normality and $φ$-normality of holomorphic functions in several complex variables

Abstract

In this paper, we investigate $φ$-normal functions and normal families of holomorphic functions concerning total derivatives in $\mathbb{C}^{n}.$ More precisely, we prove a sufficient condition for a holomorphic function defined on an open unit ball in $\mathbb{C}^{n}$ satisfying certain conditions involving higher order partial derivatives to be $φ$-normal. Furthermore, by using differential inequalities involving total differential polynomials in $\mathbb{C}^{n}$, we establish some normality criteria for holomorphic functions in $\mathbb{C}^{n}$ which generalize some known results.