You-Ming WANG

5586

On normality of meromorphic functions with multiple zeros and sharing values

In this paper we study the problem of normal families of meromorphic functions concerning shared values. Let F be a family of meromorphic functions in the plane domain D \subseteq C and n be a positive integer. Let a, b be two finite complex constants such that a \neq 0. If n \geq 3 and f + a(f')n and g + a(g')n share b in D for every pair of functions f, g \in F, then F is normal in D. And some examples are provided to show the result is sharp.
Anahtar Kelimeler:

Meromorphic functions, shared value, normal family

On normality of meromorphic functions with multiple zeros and sharing values

In this paper we study the problem of normal families of meromorphic functions concerning shared values. Let F be a family of meromorphic functions in the plane domain D \subseteq C and n be a positive integer. Let a, b be two finite complex constants such that a \neq 0. If n \geq 3 and f + a(f')n and g + a(g')n share b in D for every pair of functions f, g \in F, then F is normal in D. And some examples are provided to show the result is sharp.
Keywords:

Meromorphic functions, shared value, normal family,

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Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: 6
  • Yayıncı: TÜBİTAK
Arşiv
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