Computational Methods and Function Theory 12 (2012), No. 1, 307--328
Copyright Heldermann Verlag 2012
Xiao-Min Li
xmli01267@gmail.com , Ocean University of China, Department of Mathematics, Qingdao, Shandong 266100, People's Republic of China.
We prove a result concerning the growth of solutions of a certain difference equation. We also get a uniqueness result of entire functions sharing a set with their difference operators, where the set consists of two entire functions of smaller orders. This result deals with a question given by Liu [21]. We also prove a uniqueness result of entire functions sharing a finite set with their difference operators. This is related to a question of Gross [7] concerning entire functions of finite orders sharing a finite set with their difference operators.
Keywords: Entire functions, meromorphic functions and their shifts, difference operators, uniqueness theorems.
MSC 2000: 30D35, 30D30.
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