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Normality and Montel's Theorem

Gopal Datt, Sanjay Kumar

Abstract

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 normality test in a certain sense.

Normality and Montel's Theorem

Abstract

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 normality test in a certain sense.

Paper Structure

This paper contains 2 sections, 6 theorems, 29 equations.

Table of Contents

  1. Introduction and main results
  2. Proof of Main Theorems

Key Result

Theorem 1.1

Let $\mathcal{F}$ be a family of meromorphic functions defined on a domain $D\subset\mathbb{C}$ and let $\psi\not\equiv0$ be a holomorphic function in $D$ such that zeros of $\psi(z)$ are of multiplicity at most $m$. Suppose that then $\mathcal{F}$ is normal in $D$.

Theorems & Definitions (15)

  • Example
  • Theorem 1.1
  • Corollary 1.2
  • Corollary 1.3
  • Remark 1.4
  • Example 1.5
  • Theorem 1.6
  • Example 1.7
  • Example 1.8
  • Lemma 2.1
  • ...and 5 more