UNIQUENESS RESULTS OF MEROMORPHIC FUNCTIONS WHOSE DERIVATIVES SHARE FOUR SMALL FUNCTIONS

doi:10.1016/S0252-9602(12)60126-X

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (4): 1593-1606.doi: 10.1016/S0252-9602(12)60126-X

UNIQUENESS RESULTS OF MEROMORPHIC FUNCTIONS WHOSE DERIVATIVES SHARE FOUR SMALL FUNCTIONS

李效敏^1,2|仪洪勋¹|胡海燕³

1. Department of Mathematics, Ocean University of China, Qingdao 266100, China；
2. Department of Physics and Mathematics, University of Eastern Finland, P. O. Box 111, 80101 Joensuu, Finland；
3. Department of Mathematics, Shandong University, Jinan 250100, China

收稿日期:2010-04-26 修回日期:2011-07-28 出版日期:2012-07-20 发布日期:2012-07-20
基金资助:
This work is supported by the NSFC (11171184), the NSFC (10771121), the NSFC & RFBR (Joint Project) (10911120056), the NSFC (40776006), the NSF of Shandong Province, China (Z2008A01), and the NSF of Shandong Province, China (ZR2009AM008).

UNIQUENESS RESULTS OF MEROMORPHIC FUNCTIONS WHOSE DERIVATIVES SHARE FOUR SMALL FUNCTIONS

LI Xiao-Min^1,2, YI Hong-Xun¹, HU Hai-Yan³

1. Department of Mathematics, Ocean University of China, Qingdao 266100, China；
2. Department of Physics and Mathematics, University of Eastern Finland, P. O. Box 111, 80101 Joensuu, Finland；
3. Department of Mathematics, Shandong University, Jinan 250100, China

Received:2010-04-26 Revised:2011-07-28 Online:2012-07-20 Published:2012-07-20
Supported by:
This work is supported by the NSFC (11171184), the NSFC (10771121), the NSFC & RFBR (Joint Project) (10911120056), the NSFC (40776006), the NSF of Shandong Province, China (Z2008A01), and the NSF of Shandong Province, China (ZR2009AM008).

摘要/Abstract

摘要：

We prove an oscillation theorem of two meromorphic functions whose deriva-tives share four values IM. From this we obtain some uniqueness theorems, which improve the corresponding results given by Yang [16] and Qiu [10], and supplement results given by
Nevanlinna [9] and Gundersen [3, 4]. Some examples are provided to show that the results in this paper are best possible.

关键词: Nevanlinna theory, meromorphic function, shared value, uniqueness, order of growth

Abstract:

Key words: Nevanlinna theory, meromorphic function, shared value, uniqueness, order of growth

中图分类号:

30D35

李效敏, 仪洪勋, 胡海燕. UNIQUENESS RESULTS OF MEROMORPHIC FUNCTIONS WHOSE DERIVATIVES SHARE FOUR SMALL FUNCTIONS[J]. 数学物理学报(英文版), 2012, 32(4): 1593-1606.

LI Xiao-Min, YI Hong-Xun, HU Hai-Yan. UNIQUENESS RESULTS OF MEROMORPHIC FUNCTIONS WHOSE DERIVATIVES SHARE FOUR SMALL FUNCTIONS[J]. Acta mathematica scientia,Series B, 2012, 32(4): 1593-1606.

参考文献

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[9] Nevanlinna R. Einige Eindeutigkeitss¨atze in der Theorie der meromorphen Funktionen. Acta Math, 1926, 48: 367–391

[10] Qiu G D. Four values theorem of derivatives of meromorphic functions. Sys Sci Math Sci, 1998, 11: 245–248

[11] Qiu G D. Meromorphic functions whose derivatives share four small functions. Indian J Pure Appl Math, 2002, 33: 761–767

[12] Steinmetz N. A uniqueness theorem for three meromorphic functions. Ann Acad Sci Fenn Ser A I Math, 1988, 13: 93–110

[13] Yamanoi K. The second main theorem for small functions and related problems. Acta Math, 2004, 192: 225–299

[14] Yang C C, Yi H X. Uniqueness Theory of Meromorphic Functions. Dordrecht, Boston, London: Kluwer Academic Publishers, 2003

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[16] Yang L. Precise estimate of total deficiency of meromorphic derivatives. J D'Anal Math, 1990, 55: 287–296

UNIQUENESS RESULTS OF MEROMORPHIC FUNCTIONS WHOSE DERIVATIVES SHARE FOUR SMALL FUNCTIONS

UNIQUENESS RESULTS OF MEROMORPHIC FUNCTIONS WHOSE DERIVATIVES SHARE FOUR SMALL FUNCTIONS

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