an:06644018
Zbl 1389.30138
Majumder, Sujoy
Nonlinear differential monomials sharing two values
EN
Math. Bohem. 141, No. 3, 339-361 (2016).
00360055
2016
j
30D35
meromorphic functions; differential polynomials; sharing polynomials; uniqueness problems
Summary: Using the notion of weighted sharing of values which was introduced by \textit{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 \textit{Y.-H. Cao} and \textit{X.-B. Zhang} [J. Inequal. Appl. 2012, Article ID 100 (2012; Zbl 1291.30193)].
Zbl 0981.30023; Zbl 1025.30027; Zbl 1291.30193