Abstract
Let f be a nonconstant meromorphic function such that \({\overline{N}(r, f) < \lambda T(r, f)}\), where \({\lambda \in [0, \frac{1}{9})}\), and let a, b be two distinct finite values. If f and f′ share a, b IM, then \({f \equiv f'}\).
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Gundersen G.G.: Meromorphic functions that share two finite values with their derivative. Pac. J. Math. 105, 299–309 (1983)
Hayman W.K.: Meromorphic functions. Clarendon Press, Oxford (1964)
Laine I.: Nevanlinna Theory and Complex Differential Equations. Clarendon Press, Oxford (1993)
Milloux, H.: Les fonctions méromorphes et leurs dérivées. Extension d’un théorème de R. Nevanlinna. Appl. Act. Scient. et Ind. 888, 1940.
Mues E., Steinmetz N.: Meromorphe Funktionen, die mit ihrer ableitung werte teilen. Manuscr. Math. 29, 195–206 (1979)
Mues E., Steinmetz N.: Meromorphe funktionen, die mit ihrer ableitung zwei werte teilen. Result. Math. 6, 48–55 (1983)
Rubel, L.A., Yang, C.C.: Values shared by an entire function and its derivative. Lecture Notes in Math. 599. Springer, Berlin, pp. 101–103 (1977)
Yang C.C., Yi H.X.: Uniqueness theory of meromorphic functions. Kluwer Academic publishers, The Netherlands (2003)
Yang L.: Value Distribution Theory. Springer, Berlin (1993)
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This work is supported by NNSF of China (NO. 11171013).
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Li, S. Meromorphic Functions Sharing Two Values IM with Their Derivatives. Results. Math. 63, 965–971 (2013). https://doi.org/10.1007/s00025-012-0246-x
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DOI: https://doi.org/10.1007/s00025-012-0246-x