CHARACTERISTIC FUNCTION AND DEFICIENCY OF MEROMORPHIC FUNCTIONS IN THE PUNCTURED PLANE

doi:10.1016/S0252-9602(15)30012-6

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (3): 673-680.doi: 10.1016/S0252-9602(15)30012-6

CHARACTERISTIC FUNCTION AND DEFICIENCY OF MEROMORPHIC FUNCTIONS IN THE PUNCTURED PLANE

吴昭君¹, 陈生安¹, 陈裕先²

1. School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning 437100, China;
2. School of Mathematics and Computer Science, Xinyu University, Xinyu 338004, China

收稿日期:2014-04-20 修回日期:2014-10-01 出版日期:2015-05-01 发布日期:2015-05-01
基金资助:
The first author is supported by the National Natural Science Foundation of China (11201395). The second author is supported by the Science Foundation of Educational Commission of Hubei Province (D20132804). The third author is supported by the Science Foundation of Jiangxi Province (20122BAB201006).

CHARACTERISTIC FUNCTION AND DEFICIENCY OF MEROMORPHIC FUNCTIONS IN THE PUNCTURED PLANE

Zhaojun WU¹, Sheng'an CHEN¹, Yuxian CHEN²

1. School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning 437100, China;
2. School of Mathematics and Computer Science, Xinyu University, Xinyu 338004, China

Received:2014-04-20 Revised:2014-10-01 Online:2015-05-01 Published:2015-05-01
Supported by:
The first author is supported by the National Natural Science Foundation of China (11201395). The second author is supported by the Science Foundation of Educational Commission of Hubei Province (D20132804). The third author is supported by the Science Foundation of Jiangxi Province (20122BAB201006).

摘要/Abstract

摘要：

In this article, some facts of the value distribution theory for meromorphic functions with maximal deficiency sum in the plane will be considered in the punctured plane, and also the relationship between the deficiency of meromorphic function in the punctured plane and that of their derivatives is studied.

关键词: Meromorphic function, maximal deficiency sum, punctured plane

Abstract:

Key words: Meromorphic function, maximal deficiency sum, punctured plane

中图分类号:

30D30

吴昭君, 陈生安, 陈裕先. CHARACTERISTIC FUNCTION AND DEFICIENCY OF MEROMORPHIC FUNCTIONS IN THE PUNCTURED PLANE[J]. 数学物理学报(英文版), 2015, 35(3): 673-680.

Zhaojun WU, Sheng'an CHEN, Yuxian CHEN. CHARACTERISTIC FUNCTION AND DEFICIENCY OF MEROMORPHIC FUNCTIONS IN THE PUNCTURED PLANE[J]. Acta mathematica scientia,Series B, 2015, 35(3): 673-680.

参考文献

[1] Cao T B, Deng Z S. On the uniqueness of meromorphic functions that share three or two finite sets on annuli. Proceedings Mathematical Sciences, 2012, 122(2): 203-220
[2] Cao T B, Yi H X. Uniqueness theorems of meromorphic functions shares sets IM on Annuli. Acta Math Sinica (Chin Ser), 2011, 54 (4): 623-632
[3] Cao T B, Yi H X, Xu H Y. On the multiple values and uniqueness of meromorphic functions on annuli. Comput Math Appl, 2009, 58(7): 1457-1465
[4] Chen Y X, Wu Z J. Exceptional values of meromorphic functions and of their derivatives on annuli. Ann Polon Math, 2012, 105: 154-165
[5] Edrei A. Sums of deficiencies of meromorphic functions II. J Analyse Math, 1967, 19: 53-74
[6] Fang M L. A note on a result of Singh and Kulkarni, Internat. J Math and Math Sci, 2000, 23: 285-288
[7] Fernández A. On the value distribution of meromorphic function in the punctured plane. Mathematychni Studii, 2010, 34: 136-144
[8] Goldberg A, Ostrovskii I. Value Distribution of Meromorphic Functions//Transl Math Monogr, Vol. 236. Providence, RI: American Mathematical Society, 2008; translated from the 1970 Russian original by Mikhail Ostrovskii, with an appendix by Alexandre Eremenko and James K. Langley
[9] Hayman W K. Meromorphic functions. Oxford: Oxford Mathematical Monographs Clarendon Press, 1964
[10] Khrystiyanyn A Ya, Kondratyuk A A. On the Nevanlinna Theory for meromorphic functions on annuli I. Mathematychni Studii, 2005, 23: 19-30
[11] Khrystiyanyn A Ya, Kondratyuk A A. On the Nevanlinna Theory for meromorphic functions on annuli II. Mathematychni Studii, 2005, 24: 57-68
[12] Kondratyuk A A, Laine I. Meromorphic functions in multiply connected domains//Fourier series methods in complex analysis (Mekrij¨arvi, 2005). Univ Juensuu Dept Ser, 2006, 10: 9-111
[13] Korhonen R. Nevanlinna Theory in an annulus. Value distribution theory and related topics//Adv Complex Anal and Applic. Kluwer Academic Publishers, 2004: 167-179
[14] Lahiri I. Milloux theorem and deficiency of vector-valued meromorphic functions. J Indian Math Soc, 1990, 55: 235-250
[15] Shan S M, Singh S K. On the derivative of a meromorphic function with maximum defect. Math Zeitschr, 1956, 65: 171-174
[16] Singh S K, Kulkarni V N. Characteristc function of a meromorphic function and its derivative. Ann Polon Math, 1973, 28: 123-133
[17] Weitsman Allen. Meromorphic functions with maximal deficiency sum and a conjecture of F. Nevanlinna. Acta Math, 1969, 123: 115-139
[18] Wu Z J, Chen Y X. Milloux inequality of meromorphic function in annuli. Journal of Mathematical Ineaualities, 2013, 7(4): 577-586
[19] Wu Z J. An inequality on the zeros and poles of vector valued meromorphic functions. Acta Mathematica Scientia, 2014, 34B(2): 380-386
[20] Yang L. Value distribution theory. Translated and revised from the 1982 Chinese original. Berlin: Springer- Verlag; Beijing: Science Press Beijing, 1993

CHARACTERISTIC FUNCTION AND DEFICIENCY OF MEROMORPHIC FUNCTIONS IN THE PUNCTURED PLANE

CHARACTERISTIC FUNCTION AND DEFICIENCY OF MEROMORPHIC FUNCTIONS IN THE PUNCTURED PLANE

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	Nguyen Van THIN. NORMAL FAMILY OF MEROMORPHIC FUNCTIONS SHARING HOLOMORPHIC FUNCTIONS AND THE CONVERSE OF THE BLOCH PRINCIPLE[J]. 数学物理学报(英文版), 2017, 37(3): 623-656.
[2]	高凌云. ON ENTIRE SOLUTIONS OF TWO TYPES OF SYSTEMS OF COMPLEX DIFFERENTIAL-DIFFERENCE EQUATIONS[J]. 数学物理学报(英文版), 2017, 37(1): 187-194.
[3]	陈玮, 田宏根, 扈培础. NORMAL FAMILIES OF MEROMORPHIC FUNCTIONS WITH SHARED VALUES[J]. 数学物理学报(英文版), 2016, 36(1): 87-93.
[4]	袁文俊, Weiling XIONG, Jianming LIN, Yonghong WU. ALL MEROMORPHIC SOLUTIONS OF AN AUXILIARY ORDINARY DIFFERENTIAL EQUATION AND ITS APPLICATIONS[J]. 数学物理学报(英文版), 2015, 35(5): 1241-1250.
[5]	曹红哲, 曹廷彬. TWO MEROMORPHIC FUNCTIONS SHARE SOME PAIRS OF SMALL FUNCTIONS WITH TRUNCATED MULTIPLICITIES[J]. 数学物理学报(英文版), 2014, 34(6): 1854-1864.
[6]	张继龙, 杨连中. DIFFERENTIAL POLYNOMIALS SHARING ONE VALUE[J]. 数学物理学报(英文版), 2014, 34(6): 1865-1874.
[7]	李效敏, 仪洪勋. UNIQUENESS OF MEROMORPHIC FUNCTIONS WHOSE NONLINEAR DIFFERENTIAL POLYNOMIALS SHARE ONE VALUE OR HAVE THE SAME FIXED POINTS IN AN ANGULAR DOMAIN[J]. 数学物理学报(英文版), 2014, 34(3): 593-609.
[8]	Jacek DZIOK. MEROMORPHIC FUNCTIONS WITH BOUNDED BOUNDARY ROTATION[J]. 数学物理学报(英文版), 2014, 34(2): 466-472.
[9]	Mohamed K. AOUF, Teodor BULBOACA, Rabha M. EL-ASHWASH. SUBORDINATION PROPERTIES OF MULTIVALENT FUNCTIONS INVOLVING AN EXTENDED FRACTIONAL DIFFERINTEGRAL OPERATOR[J]. 数学物理学报(英文版), 2014, 34(2): 367-379.
[10]	吴昭君. AN INEQUALITY ON THE ZEROS AND POLES OF VECTOR VALUED MEROMORPHIC FUNCTIONS[J]. 数学物理学报(英文版), 2014, 34(2): 380-386.
[11]	刘永, 祁晓光. UNIQUENESS OF DIFFERENCE POLYNOMIALS OF MEROMORPHIC FUNCTIONS[J]. 数学物理学报(英文版), 2014, 34(2): 444-452.
[12]	Muhammad ARIF, Janusz SOK′O l, Muhammad AYAZ. SUFFICIENT CONDITION FOR FUNCTIONS TO BE IN A CLASS OF MEROMORPHIC MULTIVALENT SAKAGUCHI TYPE SPIRAL-LIKE FUNCTIONS[J]. 数学物理学报(英文版), 2014, 34(2): 575-578.
[13]	雷春林, 方明亮, 曾翠萍. SOME NORMALITY CRITERIA OF MEROMORPHIC FUNCTIONS[J]. 数学物理学报(英文版), 2013, 33(6): 1667-1674.
[14]	R. M. EL-ASHWAH. SOME CONVOLUTION AND INCLUSION PROPERTIES FOR SUBCLASSES OF MEROMORPHIC p-VALENT FUNCTIONS INVOLVING INTEGRAL OPERATOR[J]. 数学物理学报(英文版), 2013, 33(6): 1749-1758.
[15]	崔巍巍, 杨连忠. ZEROS AND FIXED POINTS OF DIFFERENCE OPERATORS OF MEROMORPHIC FUNCTIONS[J]. 数学物理学报(英文版), 2013, 33(3): 773-780.