Uniqueness of meromorphic functions concerning sharing two small functions with their derivatives |
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Authors: | Linke M Dan Liu and Mingliang Fang |
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Institution: | Institute of Applied Mathematics, South China Agricultural University, Guangzhou, 510642, China,Institute of Applied Mathematics, South China Agricultural University, Guangzhou, 510642, China and Institute of Applied Mathematics, South China Agricultural University, Guangzhou, 510642, China |
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Abstract: | In this paper, we study the uniqueness of meromorphic functions that share two small functions with their derivatives. We prove the following result: Let $f$ be a nonconstant meromorphic function such that $\mathop {\overline{\lim}}\limits_{r\to\infty} \frac{\bar{N}(r,f)}{T(r,f)}<\frac{3}{128}$, and let $a$, $b$ be two distinct small functions of $f$ with $a\not\equiv\infty$ and $b\not\equiv\infty$. If $f$ and $f"$ share $a$ and $b$ IM, then $f\equiv f"$. |
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Keywords: | Meromorphic functions shared small functions derivatives |
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