Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Normality criteria for a family of meromorphic functions with multiple zeros

Gopal Datt, Yuntong Li, Poonam Rani

Abstract

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 of the results of Fang and Zalcman and Chen et al to a great extent.

Normality criteria for a family of meromorphic functions with multiple zeros

Abstract

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 of the results of Fang and Zalcman and Chen et al to a great extent.

Paper Structure

This paper contains 4 sections, 12 theorems, 90 equations.

Table of Contents

  1. Introduction and main results
  2. Some Notations and results of Nevanlinna theory
  3. Some Lemmas
  4. Proof of Main Results

Key Result

Theorem 1.1

Let $\alpha(z)\not\equiv 0$ be a holomorphic function with zeros of multiplicity at most $m$ in $D$. Let $a\in\mathbb{C}$ be a non-zero constant, and $n, k$ be positive integers such that $n>k+1$, and $m<k$. Let $\mathcal{F}$ be a family of meromorphic functions in the domain $D$. Suppose that for e

Theorems & Definitions (22)

  • Theorem 1.1
  • Theorem 1.2
  • Example
  • Theorem 1.3
  • Theorem 1.4
  • Lemma 3.1
  • Lemma 3.2
  • Lemma 3.3
  • proof
  • Lemma 3.4
  • ...and 12 more