Abstract
In this paper we shall prove that if a non-constant meromorphic f and its k-th derivative f (k) (k ≥ 2) share the value \({a\not= 0,\infty\; CM}\) (IM) and if \({\bar{N}(r,\frac{1}{f})=S(r,f)\;\left(\bar{N}\left(r,\frac{1}{f}\right)+\bar{N}\left(r,\frac{1}{f^{(k)}}\right)=S(r,f)\right)}\), then \({f \equiv f^{(k)}}\). These results extend the results in Al-Khaladi (J Al-Anbar Univ Pure Sci 3:69–73, 2009).
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Al-Khaladi A.H.H.: Meromorphic functions that share one finite value CM or IM with their first derivative. J Al-Anbar Univ. Pure Sci. 3, 69–73 (2009)
Al-Khaladi A.H.H.: On meromorphic functions that share one value with their derivative. Analysis 25, 131–140 (2005)
Al-Khaladi, A.H.H.: When meromorphic functions and its k-th derivative share one small function (Preprint)
Gundersen G.G.: Meromorphic functions that share finite values with their derivative. J. Math. Anal. Appl. 75, 441–446 (1980)
Hayman W.K.: Meromorphic Functions. Clarendon Press, Oxford (1964)
Yang C.C., Yi H.X.: Uniqueness Theory of Meromorphic Functions. Kluwer Academic Publishers, Dordrecht (2004)
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Al-Khaladi, A.H.H. Meromorphic Functions That Share One Finite Value CM or IM with Their k-th Derivative. Results. Math. 63, 95–105 (2013). https://doi.org/10.1007/s00025-011-0163-4
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DOI: https://doi.org/10.1007/s00025-011-0163-4