数学研究通讯

2019, v.35(03) 283-288

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Further Results on Meromorphic Functions and Their nth Order Exact Differences with Three Shared Values
Further Results on Meromorphic Functions and Their nth Order Exact Differences with Three Shared Values

CHEN SHENG-JIANG;XU AI-ZHU;LIN XIU-QIANG;

摘要(Abstract):

Let E(a, f) be the set of a-points of a meromorphic function f(z) counting multiplicities. We prove that if a transcendental meromorphic function f(z) of hyper order strictly less than 1 and its nth exact difference ?_c~nf(z) satisfy E(1, f) =E(1, ?_c~nf), E(0, f) ? E(0, ?_c~nf) and E(∞, f) ? E(∞, ?_c~nf), then ?_c~nf(z) ≡ f(z).This result improves a more recent theorem due to Gao et al.(Gao Z, Kornonen R,Zhang J, Zhang Y. Uniqueness of meromorphic functions sharing values with their nth order exact differences. Analysis Math., 2018, https://doi.org/10.1007/s10476-018-0605-2) by using a simple method.

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基金项目(Foundation): The NSF (11801291) of China,the NSF (2018J01424) of Fujian Province

作者(Author): CHEN SHENG-JIANG;XU AI-ZHU;LIN XIU-QIANG;

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