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Results on entire and meromorphic functions that share small function with their homogeneous and linear differential polynomials. (English) Zbl 1435.30091

Summary: Using the results of S. S. Bhoosnurmath, we mainly study the uniqueness of entire and meromorphic functions that share small functions with their homogeneous and linear differential polynomials. In this paper, we obtain significant improvements and generalizations of the results of H. X. Yi.

MSC:

30D20 Entire functions of one complex variable (general theory)
30D30 Meromorphic functions of one complex variable (general theory)
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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References:

[1] S. S. Bhoosnurmath and Smita R. K., On entire and meromorphic functions that share one small function with their differential polynomial, Int. J. Anal. (2013), Article Id 926340. · Zbl 1291.30191
[2] W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964). · Zbl 0115.06203
[3] C. C. Yang and H. X. Yi, Uniqueness theory of meromorphic functions, Kluwer, Dordrect, 2004.
[4] H. X. Yi, Uniqueness theorems for meromorphic functions whose nth derivatives share the same 1-points, Complex Var. Theory Appl., 34(1997), 421-436. · Zbl 0908.30032
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