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Normality and Sharing Functions

Gopal Datt, Sanjay Kumar

Abstract

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.

Normality and Sharing Functions

Abstract

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.

Paper Structure

This paper contains 3 sections, 7 theorems, 17 equations.

Table of Contents

  1. Introduction and Main Result
  2. Some Lemmas
  3. Proof of Theorem

Key Result

Theorem 1.2

CF 1 Let $\mathcal{F}$ be a family of meromorphic functions in a domain $\mathcal{D}$, let $k \ (\geq2)$ be an integer and $a, b, c$ are complex numbers such that $a\neq b$. If for all $f\in\mathcal{F}, \ f \ \text{and}\ f^{(k)}$ share $a, b$ and the zeros of $f-c$ are of multiplicity at least $k+1$

Theorems & Definitions (12)

  • Definition 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Theorem 1.4
  • Example 1.5
  • Example 1.6
  • Example 1.7
  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • ...and 2 more