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http://dx.doi.org/10.4134/BKMS.2009.46.6.1079

UNIQUENESS THEOREMS OF MEROMORPHIC FUNCTIONS OF A CERTAIN FORM  

Xu, Junfeng (Department of Mathematics Wuyi University)
Han, Qi (Department of Mathematics University of Houston)
Zhang, Jilong (LMIB and Department of Mathematics Beihang University)
Publication Information
Bulletin of the Korean Mathematical Society / v.46, no.6, 2009 , pp. 1079-1089 More about this Journal
Abstract
In this paper, we shall show that for any entire function f, the function of the form $f^m(f^n$ - 1)f' has no non-zero finite Picard value for all positive integers m, n ${\in}\;{\mathbb{N}}$ possibly except for the special case m = n = 1. Furthermore, we shall also show that for any two nonconstant meromorphic functions f and g, if $f^m(f^n$-1)f' and $g^m(g^n$-1)g' share the value 1 weakly, then f $\equiv$ g provided that m and n satisfy some conditions. In particular, if f and g are entire, then the restrictions on m and n could be greatly reduced.
Keywords
entire function; meromorphic function; Picard value;
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