- Volume 53 Issue 1
DOI QR Code
SHARED VALUES AND BOREL EXCEPTIONAL VALUES FOR HIGH ORDER DIFFERENCE OPERATORS
- Liao, Liangwen (Department of Mathematics Nanjing University) ;
- Zhang, Jie (College of Science China University of Mining and Technology)
- Received : 2014.11.29
- Published : 2016.01.31
In this paper, we investigate the high order difference counterpart of
uniqueness;entire function;difference equation;order
Supported by : Central Universities, NSF of China
- R. Bruck, On entire functions which share one value CM with their first derivative, Results Math. 30 (1996), no. 1-2, 21-24. https://doi.org/10.1007/BF03322176
- W. Bergweiler and J. K. Langley, Zeros of differences of meromorphic functions, Math. Proc. Cambridge Philos. Soc. 142 (2007), no. 1, 133-147. https://doi.org/10.1017/S0305004106009777
- C. X. Chen and Z. X. Chen, Entire functions and their high order differences, Taiwanese J. Math. 18 (2014), no. 3, 711-729. https://doi.org/10.11650/tjm.18.2014.3453
- Z. X. Chen and K. H. Shon, On conjecture of R. Bruck, concerning the entire function sharing one value CM with its derivative, Taiwanese J. Math. 8 (2004), no. 2, 235-244. https://doi.org/10.11650/twjm/1500407625
Y. M. Chiang and S. J. Feng, On the Nevanlinna characteristic of f(z+
$\eta$) and difference equations in the complex plane, Ramanujan J. 16 (2008), no. 1, 105-129. https://doi.org/10.1007/s11139-007-9101-1
- Y. M. Chiang and S. J. Feng, On the growth of logarithmic differences, difference quotients and logarithmic derivatives of meromorphic functions, Trans. Amer. Math. Soc. 361 (2009), no. 7, 3767-3791. https://doi.org/10.1090/S0002-9947-09-04663-7
- W. K. Hayman, Slowly growing integral and subharmonic functions, Comment. Math. Helv. 34 (1960), 75-84. https://doi.org/10.1007/BF02565929
- W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964.
- J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, and J. Zhang, Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity, J. Math. Anal. Appl. 355 (2009), no. 1, 352-363. https://doi.org/10.1016/j.jmaa.2009.01.053
- G. Gundersen, Correction to meromorphic functions that share four values, Trans. Amer. Math. Soc. 304 (1987), no. 2, 847-850.
- G. Gundersen, Finite order solutions of second order linear differential equations, Trans. Amer. Math. Soc. 305 (1988), no. 1, 415-429. https://doi.org/10.1090/S0002-9947-1988-0920167-5
- G. Gundersen and L. Z. Yang, Entire functions that share one values with one or two of their derivatives, J. Math. Anal. Appl. 223 (1998), no. 1, 88-95. https://doi.org/10.1006/jmaa.1998.5959
- E. Mues, Meromorphic functions sharing four valus, Complex Variables Theory Appl. 12 (1989), no. 1-4, 167-179.
- C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Science Press, Beijing, Second Printed in 2006.
- L. Yang, Value Distribution Theory, Springer-Verlag & Science Press, Berlin, 1993.
- J. Zhang, H. Y. Kang, and L. W. Liao, Entire functions sharing a small entire function with their difference operators, Bull. Iran. Math. Soc. accepted.