Some results on a question of Li, Yi and Li
DOI:
https://doi.org/10.24193/subbmath.2019.3.08Keywords:
Meromorphic function, shift operator, difference polynomial, uniquenessAbstract
The purpose of this paper is to study the uniqueness problems of certain difference
polynomials of meromorphic functions sharing a nonzero polynomial. The results
of this paper improve and generalize some recent results due to Li, Yi and Li [10]. Some examples have been exhibited to show that some conditions used in the paper are sharp.
References
W. Bergweiler, A. Eremenko, on the singularities of the inverse to a meromorphic function of nite order,
Rev. Mat. Iberoam, 11 (1995), 355-373.
Y. M. Chiang, S. J. Feng, On the Nevanlinna characteristic f(z + ) and dierence equations in complex
plane, Ramanujan J., 16 (2008), 105-129.
Y. M. Chiang, S. J. Feng, On the growth of logarithmic dierences, dierence quotients and logarithmic
derivatives of meromorphic functions, Trans. Amer. Math. Soc., 361 (7) (2009), 3767-3791.
J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, J. L. Zhang, Value sharing results for shifts of meromorphic
function, and sucient conditions for periodicity, J. Math. Anal. Appl., 355 (2009), 352-363.
W. K. Hayman, Picard values of meromorphic Functions and their derivatives, Ann. of Math., 70 (1959),
-42.
W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964).
I. Lahiri, Value distribution of certain dierential polynomials, Int. J. Math. Math. Sc., 28 (2001), 83-91.
I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl.,
(2001), 241-253.
I. Laine, C. C. Yang, Value distribution of dierence polynomials, Proc. Japan Acad. Ser. A, 83 (2007),
-151.
X. M. Li, H. X. Yi and W. L. Li, Value distribution of certain dierence polynomials of meromorphic
functions, Rocky Mountain. J. Math., 44 (2) (2014), 599-632.
K. Liu, X. L. Liu and T. B. Cao, Value distributions and uniqueness of dierence polynomials, Adv.
Dierence Equ., 2011 Article ID 234215, 12 pages.
K. Liu, L. Z. Yang, Value distribution of the dierence operator, Arch. Math., 92 (2009), 270-278.
S. Majumder, On the uniqueness of certain type of shift polynomial sharing a small function, Analele Univ.
de Vest Timisoara, 55(1) (2017), 99-113.
E. Mues, U
ber ein problem von Hayman, Math Z., 164 (1979), 239-259.
X. G. Qi, L. Z. Yang, K. Liu, Uniqueness and periodicity of meromorphic functions concerning the dierence
operator, Comput. Math. Appl., 60 (2010), 1739-1746.
C. C. Yang, On deciencies of dierential polynomials II, Math. Z., 125 (1972), 107-112.
C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers,
Dordrecht/Boston/London, 2003.
K. Yamanoi, The second main theorem for small functions and related problems, Acta Math., 192 (2004)
-294.
H. X. Yi, Meromorphic functions that share one or two values, Complex Var Theory Appl., 28 (1995), 1-11.
J. L. Zhang, Value distribution and shared sets of dierences of meromorphic functions, J. Math. Anal.
Appl., 367 (2010), 401-408.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Transfer of copyright agreement: When the article is accepted for publication, the authors and the representative of the coauthors, hereby agree to transfer to Studia Universitatis Babeș-Bolyai Mathematica all rights, including those pertaining to electronic forms and transmissions, under existing copyright laws, except for the following, which the authors specifically retain: the authors can use the material however they want as long as it fits the NC ND terms of the license. The authors have all rights for reuse according to the license.