Partial sharing of a set of meromorphic functions and normality

Öz

By using the idea of partial sharing of a set of meromorphic functions by a member of a family of meromorphic functions  and its kth derivative we obtain a normality criterion generalizing some of the earlier results on shared sets and normal families of  meromorphic functions. Further we prove a normality criterion which improves Marty’s theorem and its reverse counterpart.

Anahtar Kelimeler

• Normal families,meromorphic function,partial sharing of sets,spherical derivative

Kaynakça

1. Chang, J.M., Fang, M.L., Zalcman, L.Composite meromorphic functions and normal families. Proc. Roy. Soc. Edinburgh, Ser. A, 139, 57-72(2009).
2. Chen, J.F.Shared sets and normal families of meromorphhic fuunctions. Rocky Mountain Journal of Mathematics (5) 40, 517-524 (2010).
3. Fang, M.L.A note on sharing values and normality. Chinese J. Math. Study 29, 29-32 (1996).
4. Fang, M.L., Zalcman, L.Normal families and uniqueness theorems for entire functions. J. Math. Anal. Appl. 280, 273-283 (2003).
5. Grahl J., Nevo, S.Spherical derivatives and normal families. J. Anal. Math., 117, 119-128 (2012).
6. Hayman, W.K.Meromorphic Functions Oxford, UK: Clarendon Press. (1964).
7. Liu, X.J., Pang, X.C.Shared values and normal families. Acta Math. Sinica. 50, 409-412 (2007).
8. Pang, X., Zalcman, L.Normal families and shared values. Bull. Lond. Math. Soc. 32, 325-331 (2000).

9. Schiff, J.L.Normal Families. Springer-Verlag, New York, 1993.
10. Schwick, W.Sharing values and normality. Arch. Math. (Basel)59, 50-54 (1992). c