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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)].
##### MSC:
 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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