Browse > Article
http://dx.doi.org/10.4134/BKMS.b170072

MEROMORPHIC FUNCTIONS PARTIALLY SHARED VALUES WITH THEIR SHIFTS  

Lin, Weichuan (Department of Mathematics Ningde Normal University)
Lin, Xiuqing (Department of Mathematics Ningde Normal University)
Wu, Aidi (Department of Mathematics Shandong University)
Publication Information
Bulletin of the Korean Mathematical Society / v.55, no.2, 2018 , pp. 469-478 More about this Journal
Abstract
We prove some uniqueness theorems of nonconstant meromorphic functions partially sharing values with their shifts. As an application, we obtain a sufficient condition on periodic meromorphic functions. Moreover, some examples are given to illustrate that the conditions are sharp and necessary.
Keywords
meromorphic function; periodicity; uniqueness; partially shared value;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 X. M. Li and H. X. Yi, Meromorphic functions sharing four values with their difference operators or shifts, Bull. Korean Math. Soc. 53 (2016), no. 4, 1213-1235.   DOI
2 K. Liu, Meromorphic functions sharing a set with applications to difference equations, J. Math. Anal. Appl. 359 (2009), no. 1, 384-393.   DOI
3 K. Liu and L.-Z. Yang, Value distribution of the difference operator, Arch. Math. (Basel) 92 (2009), no. 3, 270-278.   DOI
4 M. Ozawa, On the existence of prime periodic entire functions, Kodai Math. Sem. Rep. 29 (1977/78), no. 3, 308-321.   DOI
5 K. Yamanoi, The second main theorem for small functions and related problems, Acta Math. 192 (2004), no. 2, 225-294.   DOI
6 C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Mathematics and its Applications, 557, Kluwer Academic Publishers Group, Dordrecht, 2003.
7 J. H. Zheng, Unicity theorem for period meromorphic functions that share three values, Chi. Sci. Bull. 37 (1992), no. 1, 12-15.
8 G. Brosch, Eindeutigkeitssatze fur meromrophie Funktionen, Thesis, Technical University of Aachen, 1989.
9 K. S. Charak, R. J. Korhonen, and G. Kumar, A note on partial sharing of values of meromorphic functions with their shifts, J. Math. Anal. Appl. 435 (2016), no. 2, 1241-1248.   DOI
10 S. J. Chen and W. C. Lin, Periodicity and uniqueness of meromorphic functions concerning Three sharing values, Houston J. Math. 2016, Preprint.
11 S. J. Chen and A. Z. Xu, Periodicity and unicity of meromorphic functions with three shared values, J. Math. Anal. Appl. 385 (2012), no. 1, 485-490.   DOI
12 Y. M. Chiang and S. J. Feng, On the Nevanlinna characteristic of f($z+\eta$) and di erence equations in the complex plane, Ramanujan J. 16 (2008), no. 1, 105-129.   DOI
13 R. G. Halburd and R. J. Korhonen, Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl. 314 (2006), no. 2, 477-487.   DOI
14 R. G. Halburd and R. J. Korhonen, Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math. 31 (2006), no. 2, 463-478.
15 R. G. Halburd, R. Korhonen, and K. Tohge, Holomorphic curves with shift-invariant hyperplane preimages, Trans. Amer. Math. Soc. 366 (2014), no. 8, 4267-4298.   DOI
16 J. Heittokangas, R. Korhonen, I. Laine and J. Rieppo, Value sharing results for shifts of meromorphic functions, and suffcient conditions for periodicity, J. Math. Anal. Appl. 355 (2009), no. 1, 352-363.   DOI
17 J. Heittokangas, R. Korhonen, I. Laine and J. Rieppo, Uniqueness of meromorphic functions sharing values with their shifts, Complex Var. Elliptic Equ. 56 (2011), no. 1-4, 81-92.   DOI