On one problem of uniqueness of meromorphic functions concerning small functions
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Abstract:
In this paper, we show that if two non-constant meromorphic functions $f$ and $g$ satisfy $\overline {E}(a_{j},k,f)=\overline {E}(a_{j},k,g)$ for $j=1,2,\dots ,5$, where $a_{j}$ are five distinct small functions with respect to $f$ and $g$, and $k$ is a positive integer or $\infty$ with $k\geq 14$, then $f\equiv g$. As a special case this also answers the long-standing problem on uniqueness of meromorphic functions concerning small functions.References
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Additional Information
- Hong-Xun Yi
- Affiliation: Department of Mathematics, Shandong University, Jinan 250100, People’s Republic of China
- Email: hxyi@sdu.edu.cn
- Received by editor(s): September 22, 2000
- Received by editor(s) in revised form: December 1, 2000
- Published electronically: October 17, 2001
- Additional Notes: This work was supported by the NSFC (NO. 19871050) and the RFDP (No. 98042209).
- Communicated by: Juha M. Heinonen
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1689-1697
- MSC (2000): Primary 30D35; Secondary 30D30
- DOI: https://doi.org/10.1090/S0002-9939-01-06245-1
- MathSciNet review: 1887016