Normality from one family of meromorphic functions to another through sharing of values

TL;DR

This paper proves that under certain sharing conditions of three distinct values, a family of meromorphic functions is normal, extending and sharpening previous results in complex analysis.

Contribution

It establishes a new criterion for normality of meromorphic function families based on shared values with a normal family, improving prior theorems.

Findings

F is normal if each f in F shares three values with some g in G

The result sharpens previous theorems by Liu, Li, and Pang

Provides related sharp results in the theory of meromorphic functions

Abstract

Let F and G be two families of meromorphic functions on a domain D, and let a, b and c be three distinct points in the extended complex plane. Let G be a normal family in D such that all limit functions of G are non-constant. If for each f in F, there exists g in G such that f and g share a, b and c partially, then F is normal in D. This gives a sharp improvement of a result due to X. J. Liu, S. H. Li and X. C. Pang. We also prove some interesting related sharp results.