A result on an open problem of Lu, Li and Yang
Bull. Korean Math. Soc.
Published online June 7, 2021
Sujoy Majumder and Somnath Saha
Raiganj University
Abstract : In this paper we deal with the open problem posed by Lu, Li and Yang [11]. Mainly we have been able to solve the open problem [11] at the cost of considering the fact that f(z) is a transcendental meromorphic function of finite order having finitely many poles such that $f^{n}(z)$ and $f(z+c_{1})f(z+c_{2})\ldots f(z+c_{n})$ share 0 CM, where $n\in\mathbb{N}$ and $c_{j}\;(j=1,2,\ldots,n)\in\mathbb{C}\setminus\{0\}$.
Also we exhibit some examples to show that the conditions of our result are the best possible.
Keywords : Meromorphic function, derivative, small function
MSC numbers : 30D35
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