Photo from academic.microsoft.com
Let A>1 A > 1 be a constant, and let F F be a family of meromorphic functions in a domain D . If, for every function f∈F f ∈… Click to show full abstract
Let A>1 A > 1 be a constant, and let F F be a family of meromorphic functions in a domain D . If, for every function f∈F f ∈ F , f has only zeros of multiplicity at least 2 and satisfies the following conditions: (1) f(z)=0⇒|f ″ (z)|≤A|z| f ( z ) = 0 ⇒ | f ″ ( z ) | ≤ A | z | , (2) f ″ (z)≠z f ″ ( z ) ≠ z , (3) all poles of f have multiplicity at least 4, then F F is normal in D . In this paper, we first give an example to show that condition (3) is sharp, and prove that our counterexample is unique in some sense.
Keywords:
normality criterion;
families meromorphic;
meromorphic functions;
counterexample normality;
criterion families
Journal Title: Comptes Rendus Mathematique
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!
Journal Title: Comptes Rendus Mathematique
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!