Acta mathematica scientia, Series B >
UNIQUENESS OF DIFFERENCE POLYNOMIALS OF MEROMORPHIC FUNCTIONS
Received date: 2012-09-09
Revised date: 2013-10-16
Online published: 2014-03-20
Supported by
This work was supported by the National Nat-ural Science Foundation of China (10771121, 11301220, 11371225) and the Tianyuan Fund for Mathematics (11226094), the NSF of Shandong Province, China (ZR2012AQ020, ZR2010AM030), the Fund of Doctoral Pro-gram Research of Shaoxing College of Art and Science (20135018), and the Fund of Doctoral Program Research of University of Jinan (XBS1211).
In this article, we investigate the uniqueness problems of difference polynomials of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Shibazaki. Some examples are given to show the results in this article are best possible.
Key words： Meromorphic functions; difference polynomials; uniqueness; finite order
LIU Yong , QI Xiao-Guang . UNIQUENESS OF DIFFERENCE POLYNOMIALS OF MEROMORPHIC FUNCTIONS[J]. Acta mathematica scientia, Series B, 2014 , 34(2) : 444 -452 . DOI: 10.1016/S0252-9602(14)60018-7
[1] Chiang Y M, Feng S J. On the Nevanlinna characteristic of f(z+) and difference equations in the complex plane. Ramanujan J, 2008, 16: 105–129
[2] Chen Z X, Yi H X. On sharing values of meromorphic functions and their differences. Results Math, 2013, 63: 557–565
[3] Goldberg A A, Ostrovskii I V. Distribution of Values of Meromorphic Functions. Mosow: Nauka, 1970
[4] Halburd R G, Korhonen R. Nevanlinna theory for the difference operator. Ann Acad Sci Fenn Math, 2006, 94: 463–478
[5] Halburd R G, Korhonen R. Difference analogue of the lemma on the logarithmic derivative with applications to difference equatons. J Math Anal Appl, 2006, 314: 477–487
[6] Halburd R G, Korhonen R. Finite order solutions and the discrete Painlev´e equations. Proc London Math Soc, 2007, 94: 443–474
[7] Halburd R G, Korhonen R. Meromorphic solutions of difference equations, integrability and the discrete Painlev´e equations. J- Phys A, 2007, 40: 1–38
[8] Hayman W K. Meromorphic Functions. Oxford: Clarendon Press, 1964
[9] Heittokangas J, Korhonen R, Laine I, et al. Value sharing results for shift of meromorphic functions, and suffient conditions for periodicity. J Math Anal Appl, 2009, 355: 352–363
[10] Heittokangas J, Korhonen R, Laine I, Rieppo. Uniqueness of meromorphic functions sharing values with their shifts. Complex Var Elliptic Equ, 2011, 56: 81–92
[11] Liu K, Yang L Z. Value distribution of the difference operator. Arch Math, 2009, 92: 270–278
[12] Li J T, Gu Y X. On uniqueness of meromorphic functions and their derivatives. Acta Math Sinica, 2000, 43(1): 87–94
[13] Shibazaki K. Unicity theorem for entire functions of finite order. Japan Men Nat Defense Acad, 1981, 21: 61–71
[14] Yang C C, Yi H X. Uniqueness Theory of Meromorphic Function. Dordrecht: Kluwer, 2003
[15] Yang C C. On two entire functions which together with their first derivative have the same zeros. J Math Anal Appl, 1976, 56(1): 1–6
[16] Yi H X. Uniqueness theorems for meromorphic functions whose N-th derivatives share the same 1-points. Complex variables, 1997, 3(4): 421–436
/
| 〈 |
|
〉 |