Title:
|
Properties of differences of meromorphic functions (English) |
Author:
|
Chen, Zong-Xuan |
Author:
|
Shon, Kwang Ho |
Language:
|
English |
Journal:
|
Czechoslovak Mathematical Journal |
ISSN:
|
0011-4642 (print) |
ISSN:
|
1572-9141 (online) |
Volume:
|
61 |
Issue:
|
1 |
Year:
|
2011 |
Pages:
|
213-224 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
Let $f$ be a transcendental meromorphic function. We propose a number of results concerning zeros and fixed points of the difference $g(z)=f(z+c)-f(z)$ and the divided difference $g(z)/f(z)$. (English) |
Keyword:
|
meromorphic function |
Keyword:
|
difference |
Keyword:
|
divided difference |
Keyword:
|
zero |
Keyword:
|
fixed point |
MSC:
|
30C15 |
MSC:
|
30D35 |
MSC:
|
39A10 |
MSC:
|
39B32 |
idZBL:
|
Zbl 1224.30156 |
idMR:
|
MR2782770 |
DOI:
|
10.1007/s10587-011-0008-z |
. |
Date available:
|
2011-05-23T12:43:25Z |
Last updated:
|
2020-07-03 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141529 |
. |
Reference:
|
[1] Ablowitz, M., Halburd, R. G., Herbst, B.: On the extension of Painlevé property to difference equations.Nonlinearity 13 (2000), 889-905. MR 1759006, 10.1088/0951-7715/13/3/321 |
Reference:
|
[2] Bergweiler, W., Langley, J. K.: Zeros of differences of meromorphic functions.Math. Proc. Camb. Phil. Soc. 142 (2007), 133-147. Zbl 1114.30028, MR 2296397, 10.1017/S0305004106009777 |
Reference:
|
[3] Bergweiler, W., Eremenko, A.: On the singularities of the inverse to a meromorphic function of finite order.Rev. Mat. Iberoamericana 11 (1995), 355-373. Zbl 0830.30016, MR 1344897, 10.4171/RMI/176 |
Reference:
|
[4] Chen, Z. X., Shon, K. H.: On zeros and fixed points of differences of meromorphic functions.J. Math. Anal. Appl. 344-1 (2008), 373-383. Zbl 1144.30012, MR 2416313 |
Reference:
|
[5] Chiang, Y. M., Feng, S. J.: On the Nevanlinna characteristic of $f(z+\eta)$ and difference equations in the complex plane.Ramanujan J. 16 (2008), 105-129. Zbl 1152.30024, MR 2407244, 10.1007/s11139-007-9101-1 |
Reference:
|
[6] Clunie, J., Eremenko, A., Rossi, J.: On equilibrium points of logarithmic and Newtonian potentials.J. London Math. Soc. 47-2 (1993), 309-320. Zbl 0797.31002, MR 1207951 |
Reference:
|
[7] Conway, J. B.: Functions of One Complex Variable.New York, Spring-Verlag. Zbl 0887.30003, MR 0503901 |
Reference:
|
[8] Eremenko, A., Langley, J. K., Rossi, J.: On the zeros of meromorphic functions of the form $\sum\nolimits_{k=1}^{\infty}{a_k}/(z-z_k)$.J. Anal. Math. 62 (1994), 271-286. MR 1269209, 10.1007/BF02835958 |
Reference:
|
[9] Gundersen, G.: Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates.J. London Math. Soc. 37-2 (1988), 88-104. Zbl 0638.30030, MR 0921748 |
Reference:
|
[10] Halburd, R. G., Korhonen, R.: Difference analogue of the lemma on the logarithmic derivative with applications to difference equations.J. Math. Anal. Appl. 314 (2006), 477-487. Zbl 1085.30026, MR 2185244, 10.1016/j.jmaa.2005.04.010 |
Reference:
|
[11] Halburd, R. G., Korhonen, R.: Nevanlinna theory for the difference operator.Ann. Acad. Sci. Fenn. Math. 31 (2006), 463-478. Zbl 1108.30022, MR 2248826 |
Reference:
|
[12] Hayman, W. K.: Meromorphic Functions.Oxford, Clarendon Press (1964). Zbl 0115.06203, MR 0164038 |
Reference:
|
[13] Hayman, W. K.: Slowly growing integral and subharmonic functions.Comment. Math. Helv. 34 (1960), 75-84. Zbl 0123.26702, MR 0111839, 10.1007/BF02565929 |
Reference:
|
[14] Heittokangas, J., Korhonen, R., Laine, I., Rieppo, J., Tohge, K.: Complex difference equations of Malmquist type.Comput. Methods Funct. Theory 1 (2001), 27-39. Zbl 1013.39001, MR 1931600, 10.1007/BF03320974 |
Reference:
|
[15] Hinchliffe, J. D.: The Bergweiler-Eremenko theorem for finite lower order.Results Math. 43 (2003), 121-128. Zbl 1036.30022, MR 1962854, 10.1007/BF03322728 |
Reference:
|
[16] Ishizaki, K., Yanagihara, N.: Wiman-Valiron method for difference equations.Nagoya Math. J. 175 (2004), 75-102. Zbl 1070.39002, MR 2085312, 10.1017/S0027763000008916 |
Reference:
|
[17] Laine, I.: Nevanlinna Theory and Complex Differential Equations.Berlin, W. de Gruyter (1993). MR 1207139 |
Reference:
|
[18] Yang, L.: Value Distribution Theory.Beijing, Science Press (1993). Zbl 0790.30018, MR 1301781 |
Reference:
|
[19] Yang, C. C., Yi, H. X.: Uniqueness Theory of Meromorphic Functions.Dordrecht, Kluwer Academic Publishers Group (2003). Zbl 1070.30011, MR 2105668 |
. |