Journals / Turkish Journal of Mathematics / 2012 / Cilt: 36 - Sayı: 2
On normality of meromorphic functions with multiple zeros and sharing values
- Pages
- 263–271
- DOI
- —
Abstract
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.
Özet
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.