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Unicity Theorems for Meromorphic Functions and their Derivatives

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Abstract

Let f be a non-constant meromorphic function satisfying f f′ ≠ 0, and let a α ≢ 0 be a small function related to f. If f(z) = a(z) whenever f′(z) = a(z), then either f ≡ f′ or f(z) = 2a/(1 − ce −2z), where a, c are two non-zero constants and a(z) ≡ a.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing Normal University, Nanjing, 210097

    Jianming Chang

  2. Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu, 215500, P. R. China

    Jianming Chang

  3. Department of Applied Mathematics, South China Agricultural University, Guangzhou, 510642, P. R. China

    Mingliang Fang & Degui Yang

Authors
  1. Jianming Chang
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  2. Mingliang Fang
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  3. Degui Yang
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Correspondence to Jianming Chang.

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Chang, J., Fang, M. & Yang, D. Unicity Theorems for Meromorphic Functions and their Derivatives. Comput. Methods Funct. Theory 4, 299–314 (2005). https://doi.org/10.1007/BF03321071

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