Virender SİNGH, Banarsi LAL, K.s. CHARAK, Shittal SHARMA

Partial sharing of a set of meromorphic functions and normality

ISSN: 2147-5520
Başlangıç: 2015
Yayıncı: Biska Bilişim

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.

Keywords:

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

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Chang, J.M., Fang, M.L., Zalcman, L.Composite meromorphic functions and normal families. Proc. Roy. Soc. Edinburgh, Ser. A, 139, 57-72(2009).
Chen, J.F.Shared sets and normal families of meromorphhic fuunctions. Rocky Mountain Journal of Mathematics (5) 40, 517-524 (2010).
Fang, M.L.A note on sharing values and normality. Chinese J. Math. Study 29, 29-32 (1996).
Fang, M.L., Zalcman, L.Normal families and uniqueness theorems for entire functions. J. Math. Anal. Appl. 280, 273-283 (2003).
Grahl J., Nevo, S.Spherical derivatives and normal families. J. Anal. Math., 117, 119-128 (2012).
Hayman, W.K.Meromorphic Functions Oxford, UK: Clarendon Press. (1964).
Liu, X.J., Pang, X.C.Shared values and normal families. Acta Math. Sinica. 50, 409-412 (2007).
Pang, X., Zalcman, L.Normal families and shared values. Bull. Lond. Math. Soc. 32, 325-331 (2000).
Schiff, J.L.Normal Families. Springer-Verlag, New York, 1993.
Schwick, W.Sharing values and normality. Arch. Math. (Basel)59, 50-54 (1992). c