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

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【作者】 CHEN SHENG-JIANGXU AI-ZHULIN XIU-QIANG

【Author】 CHEN SHENG-JIANG;XU AI-ZHU;LIN XIU-QIANG;Department of Mathematics, Ningde Normal University;

【机构】 Department of Mathematics, Ningde Normal University

【摘要】 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.

【基金】 The NSF (11801291) of China,the NSF (2018J01424) of Fujian Province
  • 【DOI】10.13447/j.1674-5647.2019.03.09
  • 【分类号】O174.52
  • 【下载频次】4
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