Properties of differences of meromorphic functions

Zong-Xuan Chen; Kwang Ho Shon

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 1, page 213-224
  • ISSN: 0011-4642

Abstract

top
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 ) .

How to cite

top

Chen, Zong-Xuan, and Shon, Kwang Ho. "Properties of differences of meromorphic functions." Czechoslovak Mathematical Journal 61.1 (2011): 213-224. <http://eudml.org/doc/196838>.

@article{Chen2011,
abstract = {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 $g(z)/f(z)$.},
author = {Chen, Zong-Xuan, Shon, Kwang Ho},
journal = {Czechoslovak Mathematical Journal},
keywords = {meromorphic function; difference; divided difference; zero; fixed point; meromorphic function; divided difference; zero; fixed point},
language = {eng},
number = {1},
pages = {213-224},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Properties of differences of meromorphic functions},
url = {http://eudml.org/doc/196838},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Chen, Zong-Xuan
AU - Shon, Kwang Ho
TI - Properties of differences of meromorphic functions
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 1
SP - 213
EP - 224
AB - 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 $g(z)/f(z)$.
LA - eng
KW - meromorphic function; difference; divided difference; zero; fixed point; meromorphic function; divided difference; zero; fixed point
UR - http://eudml.org/doc/196838
ER -

References

top
  1. Ablowitz, M., Halburd, R. G., Herbst, B., 10.1088/0951-7715/13/3/321, Nonlinearity 13 (2000), 889-905. (2000) MR1759006DOI10.1088/0951-7715/13/3/321
  2. Bergweiler, W., Langley, J. K., 10.1017/S0305004106009777, Math. Proc. Camb. Phil. Soc. 142 (2007), 133-147. (2007) Zbl1114.30028MR2296397DOI10.1017/S0305004106009777
  3. Bergweiler, W., Eremenko, A., 10.4171/RMI/176, Rev. Mat. Iberoamericana 11 (1995), 355-373. (1995) Zbl0830.30016MR1344897DOI10.4171/RMI/176
  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. (2008) Zbl1144.30012MR2416313
  5. Chiang, Y. M., Feng, S. J., 10.1007/s11139-007-9101-1, Ramanujan J. 16 (2008), 105-129. (2008) Zbl1152.30024MR2407244DOI10.1007/s11139-007-9101-1
  6. Clunie, J., Eremenko, A., Rossi, J., On equilibrium points of logarithmic and Newtonian potentials, J. London Math. Soc. 47-2 (1993), 309-320. (1993) Zbl0797.31002MR1207951
  7. Conway, J. B., Functions of One Complex Variable, New York, Spring-Verlag. Zbl0887.30003MR0503901
  8. Eremenko, A., Langley, J. K., Rossi, J., 10.1007/BF02835958, J. Anal. Math. 62 (1994), 271-286. (1994) MR1269209DOI10.1007/BF02835958
  9. Gundersen, G., Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates, J. London Math. Soc. 37-2 (1988), 88-104. (1988) Zbl0638.30030MR0921748
  10. Halburd, R. G., Korhonen, R., 10.1016/j.jmaa.2005.04.010, J. Math. Anal. Appl. 314 (2006), 477-487. (2006) Zbl1085.30026MR2185244DOI10.1016/j.jmaa.2005.04.010
  11. Halburd, R. G., Korhonen, R., Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math. 31 (2006), 463-478. (2006) Zbl1108.30022MR2248826
  12. Hayman, W. K., Meromorphic Functions, Oxford, Clarendon Press (1964). (1964) Zbl0115.06203MR0164038
  13. Hayman, W. K., 10.1007/BF02565929, Comment. Math. Helv. 34 (1960), 75-84. (1960) Zbl0123.26702MR0111839DOI10.1007/BF02565929
  14. Heittokangas, J., Korhonen, R., Laine, I., Rieppo, J., Tohge, K., 10.1007/BF03320974, Comput. Methods Funct. Theory 1 (2001), 27-39. (2001) Zbl1013.39001MR1931600DOI10.1007/BF03320974
  15. Hinchliffe, J. D., 10.1007/BF03322728, Results Math. 43 (2003), 121-128. (2003) Zbl1036.30022MR1962854DOI10.1007/BF03322728
  16. Ishizaki, K., Yanagihara, N., 10.1017/S0027763000008916, Nagoya Math. J. 175 (2004), 75-102. (2004) Zbl1070.39002MR2085312DOI10.1017/S0027763000008916
  17. Laine, I., Nevanlinna Theory and Complex Differential Equations, Berlin, W. de Gruyter (1993). (1993) MR1207139
  18. Yang, L., Value Distribution Theory, Beijing, Science Press (1993). (1993) Zbl0790.30018MR1301781
  19. Yang, C. C., Yi, H. X., Uniqueness Theory of Meromorphic Functions, Dordrecht, Kluwer Academic Publishers Group (2003). (2003) Zbl1070.30011MR2105668

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.