Bull. Korean Math. Soc. 2017; 54(4): 1159-1171
Online first article May 18, 2017 Printed July 31, 2017
https://doi.org/10.4134/BKMS.b160238
Copyright © The Korean Mathematical Society.
Van An Nguyen and Duc Quang Si
Banking Academy, Hanoi National University of Education
The purpose of this paper is twofold. The first is to show that two meromorphic functions $f$ and $g$ must be linked by a quasi-M\"{o}bius transformation if they share a pair of small functions regardless of multiplicity and share other three pairs of small functions with multiplicities truncated to level 4. We also show a quasi-M\"{o}bius transformation between two meromorphic functions if they share four pairs of small functions with multiplicities truncated by $4$, where all zeros with multiplicities at least $k> 865$ are omitted. Moreover the explicit M\"{o}bius-transformation between such $f$ and $g$ is given. Our results are improvement of some recent results.
Keywords: meromorphic function, small function, M\"{o}bius transformation
MSC numbers: Primary 32H30, 32A22; Secondary 30D35
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