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Meromorphic Functions Sharing Three Values with their Difference Operators

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Abstract

In this work, we focus on a conjecture on the uniqueness problem of meromorphic functions sharing three distinct values with their difference operators, which is mentioned in Chen and Yi (Results Math 63, 557–565, 2013). We prove that the conjecture is true for meromorphic functions of finite order. Furthermore, a result of Zhang and Liao (Sci China Math 57, 2143–2152, 2014) is generalized from entire functions to meromorphic functions.

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Acknowledgments

The authors are greatly indebted to the referee for constructive comments, especially for Lemma 1.1 that simplifies our proofs. The authors also want thank Dr. Qi Han for pointing out some papers of interest [4, 5] which we were unaware of.

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Authors and Affiliations

  1. College of Science, China University of Petroleum, Qingdao, Shandong, 266580, People’s Republic of China

    Feng Lü & Weiran Lü

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  1. Feng Lü
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  2. Weiran Lü
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Correspondence to Feng Lü.

Additional information

Communicated by R. Korhonen.

The research was supported by NNSF of China No. 11601521 and the Fundamental Research Fund for Central Universities in China No. 15CX05061A, 15CX05063A and 15CX08011A.

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Lü, F., Lü, W. Meromorphic Functions Sharing Three Values with their Difference Operators. Comput. Methods Funct. Theory 17, 395–403 (2017). https://doi.org/10.1007/s40315-016-0188-5

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  • DOI: https://doi.org/10.1007/s40315-016-0188-5

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