Related papers: On the value distribution of a Differential Monomi…

Let $f$ be a transcendental meromorphic function defined in the complex plane $\mathbb{C}$. We consider the value distribution of the differential polynomial $f^{q_{0}}(f^{(k)})^{q_{k}}$, where $q_{0}(\geq 2), q_{k}(\geq 1)$ are $k(\geq1)$…

Let $f$ be a transcendental meromorphic function, defined in the complex plane $\mathbb{C}$. In this paper, we give a quantitative estimations of the characteristic function $T(r,f)$ in terms of the counting function of a homogeneous…

In this paper, we will consider normality and uniqueness property of a family $\mathcal{F}$ of meromorphic functions when $[Q(f)]^{(k)}$ and $[Q(g)]^{(k)}$ share $\alpha$ ignoring multiplicities, for any $f,g\in \mathcal{F}$, where $Q$ is a…

In this article we prove some normality criteria for a family of meromorphic functions which involves sharing of a non-zero value by certain differential monomials generated by the members of the family. These results generalizes some of…

Let $\mathfrak{f}$ be a transcendental entire function with hyper-order less than one. The aim of this note is to study the value distribution of the differential-difference monomials $\alpha \mathfrak{f}(z)^{q_0}(\mathfrak{f}(z+c))^{q_1}$,…

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…

Let $f$ be a transcendental meromorphic function in the complex plane $\mathbb{C}$, and $a$ be a nonzero complex number . We give quantitative estimates for the characteristic function $T(r,f)$ in terms of $N(r,1/(f^l(f^{(k)})^n-a))$, for…

A fundamental result of Lappan [Comment. Math. Helv. \textbf{49} (1974), 492-495.] states that a meromorphic function $f$ in the unit disk $\mathbb{D}$ is normal if and only if its spherical derivative is bounded on a five-point subset $E…

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…

In this paper, we prove some value distribution results which lead to some normality criteria for a family of analytic functions. These results improve some recent results.

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.

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…

Let F be a family of functions meromorphic in a domain D. If {|f|/(1+|f|^3):f in F} is locally uniformly bounded away from zero, then F is normal.

In this paper, we present a function-sharing criterion for the normality of meromorphic functions. Let $f$ be a meromorphic function in the unit disc $\mathbb{D}\subset \mathbb{C}$, $\psi_1$, $\psi_2$, and $\psi_3$ be three meromorphic…

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…

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…

This paper investigates the value distribution and growth properties of linear total differential polynomials $\mathcal{L}_k[D]f$ for meromorphic functions in several complex variables $\mathbb{C}^n$. By extending the classical Milloux…

In this paper, we prove some normality criteria concerning transitivity of normality from one family of meromorphic functions to another which improve and generalize some recent results. We also prove some value distribution results for…

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…