Abstract
In this paper we study the problem of uniqueness of meromorphic functions f(z) that share two values with \(g(z)=a_{1}(z)f(z)+a_{2}(z)f^{(k)}(z)\), where \(a_{1}(z) (\not \equiv 1, \infty )\) and \(a_{2}(z)(\not \equiv 0, \infty )\) are small functions with respect to f and obtain some results which improve and generalize the result due to Yao and Li (J Math Anal Appl 322:133–145, 2006). We also solve an open problem as posed in Liu and Qi (Kyungpook Math J 49:235–243, 2009). In this paper we provide some examples to show that the conditions in our results are the best possible.
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Majumder, S. Uniqueness of meromorphic functions sharing one or two small functions with its derivative. Rend. Circ. Mat. Palermo, II. Ser 66, 413–427 (2017). https://doi.org/10.1007/s12215-016-0259-5
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DOI: https://doi.org/10.1007/s12215-016-0259-5