ON FIXED POINTS OF MEROMORPHIC FUNCTIONS f(z) AND f(z + c),∆cf(z)

doi:10.1007/s10473-019-0507-9

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (5): 1277-1289.doi: 10.1007/s10473-019-0507-9

ON FIXED POINTS OF MEROMORPHIC FUNCTIONS f(z) AND f(z + c),∆_cf(z)

蓝双婷¹, 陈宗煊²

1. School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510665, China;
2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

收稿日期:2018-05-16 修回日期:2018-08-07 出版日期:2019-10-25 发布日期:2019-11-11
通讯作者: Zongxuan CHEN E-mail:chzx@vip.sina.com
作者简介:Shuangting LAN,E-mail:wqh200811@126.com
基金资助:
The project was supported by the Natural Science Foundation of Guangdong Province in China (2016A030310106), the National Natural Science Foundation of China (11801110, 11771090, 11761035, 11871260), the Foundation of Guangzhou Civil Aviation College (17X0419).

ON FIXED POINTS OF MEROMORPHIC FUNCTIONS f(z) AND f(z + c),∆_cf(z)

Shuangting LAN¹, Zongxuan CHEN²

1. School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510665, China;
2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

Received:2018-05-16 Revised:2018-08-07 Online:2019-10-25 Published:2019-11-11
Contact: Zongxuan CHEN E-mail:chzx@vip.sina.com
Supported by:
The project was supported by the Natural Science Foundation of Guangdong Province in China (2016A030310106), the National Natural Science Foundation of China (11801110, 11771090, 11761035, 11871260), the Foundation of Guangzhou Civil Aviation College (17X0419).

摘要/Abstract

摘要： Let c be a nonzero constant and f(z) be a transcendental meromorphic function of finite order. Under some conditions, we study the relationships between the exponent of convergence of fixed points of f(z), its shift f(z +c) and forward differences ∆_cⁿ f(z), n ∈ N⁺.

关键词: fixed points, meromorphic function, differences

Abstract: Let c be a nonzero constant and f(z) be a transcendental meromorphic function of finite order. Under some conditions, we study the relationships between the exponent of convergence of fixed points of f(z), its shift f(z +c) and forward differences ∆_cⁿ f(z), n ∈ N⁺.

Key words: fixed points, meromorphic function, differences

中图分类号:

30D35

蓝双婷, 陈宗煊. ON FIXED POINTS OF MEROMORPHIC FUNCTIONS f(z) AND f(z + c),∆_cf(z)[J]. 数学物理学报(英文版), 2019, 39(5): 1277-1289.

Shuangting LAN, Zongxuan CHEN. ON FIXED POINTS OF MEROMORPHIC FUNCTIONS f(z) AND f(z + c),∆_cf(z)[J]. Acta mathematica scientia,Series B, 2019, 39(5): 1277-1289.

参考文献

[1] Ablowitz M, Halburd R G, Herbst B. On the extension of Painlevé property to difference equations. Nonlinearty, 2000, 13:889-905
[2] Bergweiler W, Langley J K. Zeros of differences of meromorphic functions. Math Proc Camb Phil Soc, 2007, 142:133-147
[3] Bergweiler W, Pang X C. On the derivative of meromorphic function with multiple zeros. J Math Anal Appl, 2003, 278:285-292
[4] Chen Z X. Fixed points of meromorphic functions and their differences, shifts. Annales Polonici Math, 2013, 109(2):153-163
[5] Chen Z X, Shon K H. On existence of solutions of difference Riccati equation. Acta Math Sci, 2019, 39B(1):1-9
[6] Chen Z X, Shon K H. On zeros and fixed points of differences of meromorphic functions. J Math Anal Appl, 2008, 344:373-383
[7] Chen Z X, Shon K H. Properties of differnces of meromorphic functions. Czechoslovak Math J, 2011, 61(136):213-224
[8] Chiang Y M, Feng S J. On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane. Ramanujan J, 2008, 16:105-129
[9] Halburd R G, Korhonen R J. Difference analogue of the lemma on the logarithmic derivative with applications to difference equations. J Math Anal Appl, 2006, 314:477-487
[10] Halburd R G, Korhonen R J. Meromorphic solution of difference equation, integrability and the discrete Painlevé equations. J Phys A:Math Theor, 2007, 40:1-38
[11] Hayman W K. Meromorphic Functions. Oxford:Clarendon Press, 1964
[12] Heittokangas J, Korhonen R, Laine I, et al. Value sharing results for shifts of meromorphic functions, and suffcient conditions for periodicity. J Math Anal Appl, 2009, 355:352-363
[13] Ishizaki K. On difference Riccati equations and second order linear difference equations. Aequat Math, 2011, 81:185-198
[14] Laine I, Yang C C. Clunie theorems for difference and q-difference polynomials. J Lond Math Soc, 2007, 76(3):556-566
[15] Lan S T, Chen Z X. Properties of difference Painlevé IV equations. Acta Math Sci, 2017, 37B(6):1830-1840
[16] Yang L. Value Distribution Theory and Its New Research (in Chinese). Beijing:Science Press, 1982
[17] Zhang R R, Chen Z X. On meromorphic solutions of Riccati and linear difference equations. Acta Math Sci, 2013, 33B(5):1243-1254

ON FIXED POINTS OF MEROMORPHIC FUNCTIONS f(z) AND f(z + c),∆_cf(z)

ON FIXED POINTS OF MEROMORPHIC FUNCTIONS f(z) AND f(z + c),∆_cf(z)

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 0

[1]	Tarun Kumar CHAKRA, Gorachand CHAKRABORTY, Tarakanta NAYAK. HERMAN RINGS WITH SMALL PERIODS AND OMITTED VALUES[J]. 数学物理学报(英文版), 2018, 38(6): 1951-1965.
[2]	袁益让, 程爱杰, 羊丹平, 李长峰, 杨青. CONVERGENCE ANALYSIS OF MIXED VOLUME ELEMENT-CHARACTERISTIC MIXED VOLUME ELEMENT FOR THREE-DIMENSIONAL CHEMICAL OIL-RECOVERY SEEPAGE COUPLED PROBLEM[J]. 数学物理学报(英文版), 2018, 38(2): 519-545.
[3]	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.
[4]	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.
[5]	Dhananjay GOPAL, Mujahid ABBAS, Deepesh Kumar PATEL, Calogero VETRO. FIXED POINTS OF α-TYPE F-CONTRACTIVE MAPPINGS WITH AN APPLICATION TO NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION[J]. 数学物理学报(英文版), 2016, 36(3): 957-970.
[6]	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.
[7]	袁益让, 程爱杰, 羊丹平, 李长峰. THEORY AND APPLICATION OF FRACTIONAL STEP CHARACTERISTIC FINITE DIFFERENCE METHOD IN NUMERICAL SIMULATION OF SECOND ORDER ENHANCED OIL PRODUCTION[J]. 数学物理学报(英文版), 2015, 35(6): 1547-1565.
[8]	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.
[9]	Nguyen Tien DUNG. ASYMPTOTIC BEHAVIOR OF LINEAR ADVANCED DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2015, 35(3): 610-618.
[10]	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.
[11]	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.
[12]	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.
[13]	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.
[14]	Peyman SALIMI, Pasquale VETRO. A RESULT OF SUZUKI TYPE IN PARTIAL G-METRIC SPACES[J]. 数学物理学报(英文版), 2014, 34(2): 274-284.
[15]	Jacek DZIOK. MEROMORPHIC FUNCTIONS WITH BOUNDED BOUNDARY ROTATION[J]. 数学物理学报(英文版), 2014, 34(2): 466-472.