Related papers: A criterion of normality based on a single holomor…

Let $\mathcal{F}\subset\mathcal{M}(D)$ and let $a, b$ and $c$ be three distinct complex numbers. If, there exist a holomorphic function $h$ on $D$ and a positive constant $\rho$ such that for each $f\in\mathcal{F},$ $f$ and $f^{'}$…

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…

In this paper, a normality criterion concerning a sequence of meromorphic functions and their differential polynomials is obtained. Precisely, we have proved: Let $\left\{f_j\right\}$ be a sequence of meromorphic functions in the open unit…

Schwick, in [6], states that let $\mathcal{F}$ be a family of meromorphic functions on a domain $D$ and if for each $f\in\mathcal{F}$, $(f^n)^{(k)}\neq 1$, for $z\in D$, where $n, k$ are positive integers such that $n\geq k+3$, then…

In this article, we prove a normality criterion for a family of meromorphic functions which involves sharing of holomorphic functions. Our result generalizes some of the results of H. H. Chen, M. L. Fang and M. Han, Y. Gu.

In this paper we generalize a result of Ye, Pang and Yang[12] on the normality of a family of holomorphic curves in $P^N(\mathbb{C})$. Further we obtain a normality criterion for family of meromorphic functions that partially share…

We show that the family of all holomorphic functions $f$ in a domain $D$ satisfying $$\frac{|f^{(k)}|}{1+|f|}(z)\le C \qquad \mbox{ for all } z\in D$$ (where $k$ is a natural number and $C>0$) is quasi-normal. Furthermore, we give a general…

In this article, we prove a normality criterion for a family of meromorphic functions having zeros with some multiplicity which involves sharing of a holomorphic function by the members of the family. Our result generalizes Montel's…

We consider a family $\mathscr{F}$ of meromorphic functions defined in a domain $D$, a holomorphic function $\psi$ and a homogeneous differential polynomial $ P[f] $ of degree $d$ with weight $w$. In this paper, we prove the normality of…

In this paper we prove a normality criterion for the families of meromorphic functions involving sharing of functions. Our result generalizes some of the earlier results on Gu's normality criterion.

In this paper, we prove normality criteria for families of meromorphic functions involving sharing of a holomorphic function by a certain class of differential polynomials. Results in this paper extends the works of different authors…

Extension of classical Mandelbrojt's criterion for normality of a family of holomorphic zero-free functions of several complex variables is given. We show that a family of holomorphic functions of several complex variables whose…

Let F and G be two families of meromorphic functions on a domain D, and let a, b and c be three distinct points in the extended complex plane. Let G be a normal family in D such that all limit functions of G are non-constant. If for each f…

In this paper, we obtained some normality criteria for families of holomorphic functions. Which generalizes some results of Fang, Xu, Chen and Hua.

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 $D\subset \mathbb C,$ and for a…

In this paper we prove some normality criteria for a family of meromorphic functions, which involves the zeros of certain differential polynomials generated by the members of the family.

We prove that if D is a domain in C, alpha>1 and c>0, then the family F of functions meromorphic in D such that |f'(z)|/(1+|f(z)|^alpha)>c for every z in D is normalin D. For alpha=1, the same assumptions imply quasi-normality but not…

In this paper we continue our earlier investigations on normal families of meromorphic functions\cite{CS2}. Here, we prove some value distribution results which lead to some normality criteria for a family of meromorphic functions involving…

We show that a family ${\cal F}$ of meromorphic functions in a domain $D$ satisfying $$\frac{|f^{(k)}|}{1+|f^{(j)}|^\alpha}(z)\ge C \qquad \mbox{for all} z\in D \mbox{and all} f\in {\cal F}$$ (where $k$ and $j$ are integers with $k>j\ge 0$…

In this paper we prove some normality criteria for a family of meromorphic functions concerning shared analytic functions, which extend or generalized some result obtained by Y. F. Wang, M. L. Fang~\cite{WF} and J. Qui, T. Zhu ~\cite{QZ}.