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In [Israel J. Math, 2014], Grahl and Nevo obtained a significant improvement for the well-known normality criterion of Montel. They proved that for a family of meromorphic functions $mathcal F$ in a domain $Dsubset mathbb C,$ and for a positive constant $epsilon$, if for each $fin mathcal F$ there exist meromorphic functions $a_f,b_f,c_f$ such that $f$ omits $a_f,b_f,c_f$ in $D$ and $$min{rho(a_f(z),b_f(z)), rho(b_f(z),c_f(z)), rho(c_f(z),a_f(z))}geq epsilon,$$ for all $zin D$, then $mathcal F$ is normal in $D$. Here, $rho$ is the spherical metric in $widehat{mathbb C}$. In this paper, we establish the high-dimension
In this article, we prove some normality criteria for a family of meromorphic functions having zeros with some multiplicity. Our main result involves sharing of a holomorphic function by certain differential polynomials. Our results generalize some o
In this paper, we study the uniqueness of meromporphic functions and their difference operators. In particular, We have proved: Let $f$ be a nonconstant entire function on $mathbb{C}^{n}$, let $etain mathbb{C}^{n}$ be a nonzero complex number, and le
In this paper, we investigate zeros of difference polynomials of the form $f(z)^nH(z, f)-s(z)$, where $f(z)$ is a meromorphic function, $H(z, f)$ is a difference polynomial of $f(z)$ and $s(z)$ is a small function. We first obtain some inequalities f
Let ${b_{j}}_{j=1}^{k}$ be meromorphic functions, and let $w$ be admissible meromorphic solutions of delay differential equation $$w(z)=w(z)left[frac{P(z, w(z))}{Q(z,w(z))}+sum_{j=1}^{k}b_{j}(z)w(z-c_{j})right]$$ with distinct delays $c_{1}, ldots, c
We give conditions characterizing holomorphic and meromorphic functions in the unit disk of the complex plane in terms of certain weak forms of the maximum principle. Our work is directly inspired by recent results of John Wermer, and by the theory o