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

doi:10.1007/s10473-019-0507-9

Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (5): 1277-1289.doi: 10.1007/s10473-019-0507-9

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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).

Abstract

CLC Number:

30D35

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.

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[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)

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