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Some Normality Criteria

Gopal Datt, Sanjay Kumar

Abstract

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 the results of Schwick.

Some Normality Criteria

Abstract

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 the results of Schwick.

Paper Structure

This paper contains 5 sections, 15 theorems, 52 equations.

Table of Contents

  1. Introduction and main results
  2. Some Notations
  3. Some Lemmas
  4. Proof of Main Results
  5. Extensions of Theorem \ref{['thm1']} and Theorem \ref{['thm4']}

Key Result

Theorem 1.1

Let $p\neq 0$ be a complex number, $n$ be a non-negative integer and $n_1, n_2,\ldots, n_k,$$t_1, t_2,\ldots, t_k$ be positive integers. Let $\mathcal{F}$ be a family of meromorphic functions in a domain $D$ such that for every $f\in \mathcal{F}, f^n(f^{n_1})^{(t_1)}\ldots (f^{n_k})^{(t_k)}- p$ is n Then $\mathcal{F}$ is normal on $D$.

Theorems & Definitions (22)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Theorem 1.4
  • Example 1.5
  • Example 1.6
  • Example 1.7
  • Theorem 1.8
  • Remark 1.9
  • Lemma 3.1
  • ...and 12 more