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Nonlinear differential monomials sharing two values. (English) Zbl 1389.30138
Summary: Using the notion of weighted sharing of values which was introduced by I. Lahiri [Nagoya Math. J. 161, 193–206 (2001; Zbl 0981.30023); Complex Variables, Theory Appl. 46, No. 3, 241–253 (2001; Zbl 1025.30027)], we deal with the uniqueness problem for meromorphic functions when two certain types of nonlinear differential monomials namely \(\smash{h^{n}h^{(k)}}\) \((h=f,g)\) sharing a nonzero polynomial of degree less than or equal to \(3\) with finite weight have common poles and obtain two results. The results in this paper significantly rectify, improve and generalize the results due to Y.-H. Cao and X.-B. Zhang [J. Inequal. Appl. 2012, Article ID 100 (2012; Zbl 1291.30193)].
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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