DIFFERENTIAL POLYNOMIALS SHARING ONE VALUE

doi:10.1016/S0252-9602(14)60130-2

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (6): 1865-1874.doi: 10.1016/S0252-9602(14)60130-2

DIFFERENTIAL POLYNOMIALS SHARING ONE VALUE

张继龙*|杨连中

School of Mathematics &|Systems Science, Beihang University, Beijing 100191, China； School of Mathematics, Shandong University, Jinan 250100, China

收稿日期:2013-05-15 修回日期:2013-10-10 出版日期:2014-11-20 发布日期:2014-11-20
通讯作者: 张继龙，jilongzhang2007@gmail.com E-mail:jilongzhang2007@gmail.com；lzyang@sdu.edu.cn
基金资助:
This research was supported by the NNSF (11201014, 11171013, 11126036, 11371225) and the YWF-14-SXXY-008, YWF-ZY-302854 of Beihang University. This research was also supported by the youth talent program of Beijing (29201443).

DIFFERENTIAL POLYNOMIALS SHARING ONE VALUE

ZHANG Ji-Long*, YANG Lian-Zhong

School of Mathematics &|Systems Science, Beihang University, Beijing 100191, China； School of Mathematics, Shandong University, Jinan 250100, China

Received:2013-05-15 Revised:2013-10-10 Online:2014-11-20 Published:2014-11-20
Contact: ZHANG Ji-Long，jilongzhang2007@gmail.com E-mail:jilongzhang2007@gmail.com；lzyang@sdu.edu.cn
Supported by:
This research was supported by the NNSF (11201014, 11171013, 11126036, 11371225) and the YWF-14-SXXY-008, YWF-ZY-302854 of Beihang University. This research was also supported by the youth talent program of Beijing (29201443).

摘要/Abstract

摘要：

In this paper, we investigate uniqueness problems of differential polynomials of meromorphic functions. Let a, b be non-zero constants and let n, k be positive integers satisfying n ≥3k+12. If fⁿ+af^(k) and gn+ag^(k) share b CM and the b-points of fⁿ+af^(k) are not the zeros of f and g, then f and g are either equal or closely related.

关键词: meromorphic function, differential polynomial, share value

Abstract:

Key words: meromorphic function, differential polynomial, share value

中图分类号:

30D35

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.

ZHANG Ji-Long, YANG Lian-Zhong. DIFFERENTIAL POLYNOMIALS SHARING ONE VALUE[J]. Acta mathematica scientia,Series B, 2014, 34(6): 1865-1874.

参考文献

[1] Bergweiler W, Eremenko A. On the singularities of the inverse to a meromorphic function of finite order. Revista Matem´atica Iberoamerivana, 1995, 11: 355–373

[2] D¨oringer W. Exceptional values of differential polynomials. Pacific J Math, 1982, 98: 55–62

[3] Fang M L. Uniqueness and value-sharing of entire functions. Comput Math Appl, 2002, 44: 823–831

[4] Fang M L, Qiu H L. Meromorphic functions that share fixed-points. J Math Anal Appl, 2000, 268: 426–439

[5] Grahl J, Nevo S. Differential polynomials and shared values. Ann Acad Sci Fenn Math, 2011, 36: 47–70

[6] Hayman W K. Picard values of meromorphic functions and their derivatives. Ann Math, 1959, 70: 9–42

[7] Hayman W K. Meromorphic Functions. Oxford: Clarendon Press, 1964

[8] Hayman W K. Research Problems in Function Theory. The Athlone Press, 1967

[9] Jiang Yunbo, Gao Zongsheng. Normal families of meromorphic functions sharing a holomorphic function and the converse of the Bloch principle. Acta Math Sci, 2012, 32B(4): 1503–1512

[10] Laine I. Nevanlinna Theory and Complex Differential Equations. Berlin: Walter de Gruyter, 1993

[11] Li Xiaomin, Yi Hongxun. Uniqueness of meromorphic functions whose nonlinear differential polynomials share one value or have the same fixed points in an angular domain. Acta Math Sci, 2014, 34B(3): 593–609

[12] Lin W C, Yi H X. Uniqueness theorems for meromorphic function concering fixed-points. Complex Var Theory Appl, 2004, 49: 793–806

[13] Mues E. ¨Uber ein problem von Hayman. Math Z, 1979, 164: 239–259

[14] Wang Y F. On Mues conjecture and Picard values. Science in China, 1993, 36: 28–35

[15] Yang C C, Hua X H. Uniqueness and value-sharing of meromorphic functions. Ann Acad Sci Fenn Math, 1997, 22: 395–406

[16] Yang C C, Yi H X. Uniqueness Theory of Meromorphic Functions. Dordrecht: Kluwer Academic Publishers, 2003 (Chinese original: Beijing: Science Press, 1995)

[17] Yang Lianzhong, ZHang Jilong. On some results of Yi and their applications in the functional equations. Acta Math Sci, 2010, 30B(5): 1649–1660

[18] Yi H X. A question of C. C. Yang on the uniqueness of entire functions. Kodai Math J, 1990, 13: 39–46

[19] Zhang J L, Yang L Z. A power of an entire function sharing one value with its derivative. Computers and Mathematics with Applications, 2010, 60: 2153–2160

[20] Zhang J L, Gao Z S, Li S. Distribution of zeros and shared values of difference operators. Ann Polo Math, 2011, 102(3): 213–221

DIFFERENTIAL POLYNOMIALS SHARING ONE VALUE

DIFFERENTIAL POLYNOMIALS SHARING ONE VALUE

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]	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.
[6]	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.
[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.