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http://dx.doi.org/10.4134/BKMS.2013.50.4.1157

VALUE DISTRIBUTION AND UNIQUENESS ON q-DIFFERENCES OF MEROMORPHIC FUNCTIONS  

Huang, Zhi-Bo (School of Mathematical Sciences South China Normal University, Department of Physics and Mathematics University of Eastern Finland)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.4, 2013 , pp. 1157-1171 More about this Journal
Abstract
In this paper, by using the $q$-difference analogue of lemma on the logarithmic derivative lemma to re-establish some estimates of Nevanlinna characteristics of $f(qz)$, we deal with the value distribution and uniqueness of certain types of $q$-difference polynomials.
Keywords
uniqueness; q-difference polynomial; characteristic function; sharing value;
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Times Cited By KSCI : 2  (Citation Analysis)
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1 D. C. Barnett, R. G. Halburd, W. Morgan, and R. J. Korhonen, Nevanlinna theory for the q-difference operator and meromorphic solutions of q-difference equations, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), no. 3, 457-474.   DOI
2 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.   DOI
3 Z. X. Chen, Value distribution of products of meromorphic functions and their differences, Taiwanese J. Math. 15 (2011), no. 4, 1411-1421.   DOI
4 Z. X. Chen, Z. B. Huang, and X. M. Zheng, On properties of difference polynomials, Acta Math. Sci. Ser. B Engl. Ed. 31 (2011), no. 2, 627-633.
5 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   ScienceOn
6 R. G. Halburd and R. J. Korhonen, Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math. 31 (2006), no. 2, 463-478.
7 W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964.
8 J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, and J. Zhang, Value sharing results for shifts of meromorphic functions, and sufficient condition for periodicity, J. Math. Anal. Appl. 355 (2009), no. 1, 352-363.   DOI   ScienceOn
9 I. Laine and C. C. Yang, Clunie theorems for difference and q-difference polynomials, J. Lond. Math. Soc. (2) 76 (2007), no. 3, 556-566.   DOI   ScienceOn
10 I. Laine and C. C. Yang, Value distribution of difference polynomials, Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), no. 8, 148-151.   DOI
11 X. D. Luo and W. C. Lin, Value sharing results for shifts of meromorphic functions, J. Math. Anal. Appl. 377 (2011), no. 2, 441-449.   DOI   ScienceOn
12 X. G. Qi, K. Liu, and L. Z. Yang, Value sharing results of a meromorphic function f(z) and f(qz), Bull. Korean Math. Soc. 48 (2011), no. 6, 1235-1243.   과학기술학회마을   DOI   ScienceOn
13 J. F. Xu and H. X. Yi, Uniqueness of entire functions and differential polynomials, Bull. Korean Math. Soc. 44 (2007), no. 4, 623-629.   과학기술학회마을   DOI   ScienceOn
14 L. Yang, Value Distribution Theory and New Research (in Chinese), Science Press, Beijing, 1982.
15 C. C. Yang and X. H. Hua, Uniqueness and value sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math. 22 (1997), no. 2, 395-406.
16 J. L. Zhang and R. Korhonen, On the Nevanlinna characteristic of f(qz) and its application, J. Math. Anal. Appl. 369 (2010), no. 2, 537-544.   DOI   ScienceOn