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Revista de Matemática Teoría y Aplicaciones
versão impressa ISSN 1409-2433
Rev. Mat vol.22 no.2 San José Jul./Dez. 2015
Articles
Results on the uniqueness of difference polynomials of entire functions
Resultados de unicidad de diferencia de polinomios de funciones enteras
1Department of Informatics and Engineering, Jingdezhen Ceramic Institute, Jingdezhen, Jiangxi, 333403, China. E-Mail: hhhlucy2012@126.com
2Department of Informatics and Engineering, Jingdezhen Ceramic Institute, Jingdezhen, Jiangxi, 333403, China. E-Mail: xhyhhh@126.com
In this paper, we study the uniqueness of two difference polynomials of entire functions sharing one value, polynomial and small function. Our results of this paper are improvement of the previous theorems given by Chen and Chen 2, Liu, Liu and Cao 22 and Li et al. 19.
Keywords: uniqueness; entire function; difference polynomial
En este artículo, se estudia la unicidad de dos polinomios de diferencias de funciones enteras que comparten una función pequeña y polinomial. Nuestros resultados mejoran teoremas previos dados por Chen y Chen 2, Liu, Liu y Cao 22, y Li et al. 19.
Palabras clave: unicidad; función entera; polinomio de diferencias
REFERENCES
Banerjee, A. (2007) "Weighted sharing of a small function by a meromorphic function and its derivative", Comput. Math. Appl53: 1750-1761. [ Links ]
Chen, M.R., Chen, Z.X. (2012) "Properties of difference polynomials of entire functions with finite order", Chinese Ann. Math33A(3): 359-374. [ Links ]
Chiang, Y.M., Feng, S.J. (2008) "On the Nevanlinna characteristic of f(z+ η) and difference equations in the complex plane", Ramanujan J16: 105- 129. [ Links ]
Fang, C.Y., Fang, M. L. (2002). "Uniqueness of meromorphic functions and differential polynomials", Comput. Math. Appl 44: 607-617. [ Links ]
Fang, M.L., Hua, X.H. (1996). "Entire functions that share one value", J. Nanjing Unvi. Math. Biquarterly 13: 44-48. [ Links ]
Halburd, R.G., Korhonen, R.J. (2006). "Difference analogue of the lemma on the logarithmic derivative with applications to difference equations", J. Math. Anal. Appl314: 477-487. [ Links ]
Halburd, R.G., Korhonen, R.J. (2006) "Nevanlinna theory for the difference operator", Ann. Acad. Sci. Fenn. Math31: 463-478. [ Links ]
Halburd, R.G., Korhonen, R.J. (2007). "Finite-order meromorphic solutions and the discrete Painleve equations", Proc. London Math. Soc94: 443- 474. [ Links ]
Halburd, R.G., Korhonen, R.J.; Tohge, K. (2009). "Holomorphic curves with shift-invariant hyperplane preimages", Transactions of the American Mathematical Society. Available from arXiv: 0903.3236v1. http://arxiv.org/abs/0903.3236v1. [ Links ]
Hayman, W.K. (1964). Meromorphic Functions. The Clarendon Press, Oxford. [ Links ]
Heittokangas, J., Korhonen, R. J., Laine, I., Rieppo, J. (2011). "Uniqueness of meromorphic functions sharing values with their shifts", Complex Var. Elliptic Equ56: 81-92. [ Links ]
Heittokangas, J., Korhonen, R.J., Laine, I., Rieppo, J., Zhang, J.L. (2009). "Value sharing results for shifts of meromorphic fucntions, and sufficient conditions for periodicity", J. Math. Anal. Appl 355: 352-363. [ Links ]
Ishizaki, K., Tohge, K. (1997). "On the complex oscillation of some linear differential equations", J. Math. Anal. Appl 206: 503-517. [ Links ]
Lahiri, I. (2001). "Weighted sharing and uniqueness of meromorphic functions", Nagoya Math. J161: 193-206. [ Links ]
Lahiri, I. (2001). "Weighted value sharing and uniqueness of meromorphic functions", Complex Var. Elliptic Equ 46: 241-253. [ Links ]
Laine, I. (1993). Nevanlinna Theory and Domplex Differential Equations. Walter de Gruyter, Berlin-New York. [ Links ]
Laine, I., Yang, C.C. (2007). "Value distribution of difference polynomials", Proc. Japan Acad. Ser. A 83: 148-151. [ Links ]
Li, P., Wang, W.J. (2007). "Entire functions that share a small function with its derivative", J. Math. Anal. Appl 328: 743-751. [ Links ]
Li, X.M., Li, W.L., Yi, H.X., Wen, Z.T. (2011). "Uniqueness theorems of entire functions whose difference polynomials share a meromorphic function of a smaller order", Ann. Polon. Math102: 111-127. [ Links ]
Liu, K., Liu, X.L., Cao, T.B. (2012). "Some results on zeros and uniqueness of difference-differential polynomials", Appl. Math. J. Chinese Univ27(1): 94-104. [ Links ]
Liu, K. (2009) "Meromorphic functions sharing a set with applications to difference equations", J. Math. Anal. Appl 359(1): 384-393. [ Links ]
Liu, K., Liu, X.L., Cao, T.B. (2011). "Value distributions and uniqueness of difference polynomials", Advances in Difference Equations 2011, Art. ID 234215, pp.12. [ Links ]
Liu, K., Yang, L.Z. (2009). "Value distribution of the difference operator", Arch. Math92: 270-278. [ Links ]
Luo, X.D., Lin, W.C. (2011). "Value sharing results for shifts of meromorphic functions", J. Math. Anal. Appl 377: 441-449. [ Links ]
Qi, X.G. (2011). "Value distribution and uniqueness of difference polynomials and entire solutions of difference equations", Ann. Polon. Math 102: 129-142. [ Links ]
Qi, X.G., Yang, L.Z., Liu, K. (2010). "Uniqueness and periodicity of meromorphic functions concerning the difference operator", Comput. Math. Appl 60: 1739-1746. [ Links ]
Wang, X.L., Xu, H.Y., Zhan, T.S. (2014). "Properties of q-shift differencedifferential polynomials of meromorphic functions", Advances in Difference Equations2014, Art. 249, pp.16. [ Links ]
Xu, H.Y. (2013). "On the value distribution and uniqueness of difference polynomials of meromorphic functions", Advances in Difference Equations2013, Art. 90, pp.15. [ Links ]
Yang, C.C. (1972). "On deficiencies of differential polynomials", Math. Z125 (2): 107-112. [ Links ]
Yang, L. (1993). Value Distribution Theory. Springer-Verlag, Berlin. [ Links ]
Yi, H.X., Yang, C.C. (2003). Uniqueness Theory of Meromorphic Functions Kluwer Academic Publishers, Dordrecht; (1995). Chinese original: Science Press, Beijing. [ Links ]
Yi, H.X. (1999). "Meromorphic functions that share one or two values II", Kodai Math. J22: 264-272. [ Links ]
Zhang, J.L. (2010). "Value distribution and shared sets of differences of meromorphic functions", J. Math. Anal. Appl 367(2): 401-408. [ Links ]
Received: May 12, 2014; Revised: March 09, 2015; Accepted: May 06, 2015