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<p>In this paper, we primarily investigate normality problems concerning two families of functions sharing fixed points or meromorphic functions. For the normality criterion of two families of holomorphic functions sharing fixed points, we find a new idea by constructing novel auxiliary functions and employing functional transformations, thereby resolving the normality problem at the fixed point <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(z = 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>z</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>. Furthermore, in the normality criteria for two families of meromorphic functions sharing values, we generalize the shared constants in previous results to shared meromorphic functions, thus extending existing theorems.</p>

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Normal criteria for two families of meromorphic functions concerning shared functions

  • 期刊论文

  • 发表日期：

    2026年7月29日

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  • Q. Yang,
  • P. Yang,
  • X. Pang

摘要

In this paper, we primarily investigate normality problems concerning two families of functions sharing fixed points or meromorphic functions. For the normality criterion of two families of holomorphic functions sharing fixed points, we find a new idea by constructing novel auxiliary functions and employing functional transformations, thereby resolving the normality problem at the fixed point \(z = 0\) z = 0 . Furthermore, in the normality criteria for two families of meromorphic functions sharing values, we generalize the shared constants in previous results to shared meromorphic functions, thus extending existing theorems.