Palabras clave
entire function
difference polynomial
unicidad
función entera
polinomio de diferencias
Cómo citar
Resumen
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].Citas
Banerjee, A. (2007) “Weighted sharing of a small function by a meromorphic function and its derivative”, Comput. Math. Appl. 53: 1750–1761.
Chen, M.R.; Chen, Z.X. (2012) “Properties of difference polynomials of entire functions with finite order”, Chinese Ann. Math. 33A(3): 359–374.
Chiang, Y.M.; Feng, S.J. (2008) “On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane”, Ramanujan J. 16: 105–129.
Fang, C.Y.; Fang, M. L. (2002) “Uniqueness of meromorphic functions and differential polynomials”, Comput. Math. Appl. 44: 607–617.
Fang, M.L.; Hua, X.H. (1996) “Entire functions that share one value”, J. Nanjing Unvi. Math. Biquarterly 13: 44–48.
Halburd, R.G.; Korhonen, R.J. (2006) “Difference analogue of the lemma on the logarithmic derivative with applications to difference equations”, J. Math. Anal. Appl. 314: 477–487.
Halburd, R.G.; Korhonen, R.J. (2006) “Nevanlinna theory for the difference operator”, Ann. Acad. Sci. Fenn. Math. 31: 463–478.
Halburd, R.G.; Korhonen, R.J. (2007) “Finite-order meromorphic solutions and the discrete Painleve equations”, Proc. London Math. Soc. 94: 443–474.
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].
Hayman, W.K. (1964) Meromorphic Functions. The Clarendon Press, Oxford.
Heittokangas, J.; Korhonen, R. J.; Laine, I.; Rieppo, J. (2011) “Uniqueness of meromorphic functions sharing values with their shifts”, Complex Var.Elliptic Equ. 56: 81–92.
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.
Ishizaki, K.; Tohge, K. (1997) “On the complex oscillation of some linear differential equations”, J. Math. Anal. Appl. 206: 503–517.
Lahiri, I. (2001) “Weighted sharing and uniqueness of meromorphic functions”, Nagoya Math. J. 161: 193–206.
Lahiri, I. (2001) “Weighted value sharing and uniqueness of meromorphic functions”, Complex Var. Elliptic Equ. 46: 241–253.
Laine, I. (1993) Nevanlinna Theory and Domplex Differential Equations. Walter de Gruyter, Berlin-New York.
Laine, I.; Yang, C.C. (2007) “Value distribution of difference polynomials”, Proc. Japan Acad. Ser. A 83: 148–151.
Li, P.; Wang, W.J. (2007) “Entire functions that share a small function with its derivative”, J. Math. Anal. Appl. 328: 743–751.
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. Math. 102: 111–127.
Liu, K.; Liu, X.L.; Cao, T.B. (2012) “Some results on zeros and uniqueness of difference-differential polynomials”, Appl. Math. J. Chinese Univ. 27(1): 94–104.
Liu, K. (2009) “Meromorphic functions sharing a set with applications to difference equations”, J. Math. Anal. Appl. 359(1): 384–393.
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.
Liu, K.; Yang, L.Z. (2009) “Value distribution of the difference operator”, Arch. Math. 92: 270–278.
Luo, X.D.; Lin, W.C. (2011) “Value sharing results for shifts of meromorphic functions”, J. Math. Anal. Appl. 377: 441–449.
Qi, X.G. (2011) “Value distribution and uniqueness of difference polynomials and entire solutions of difference equations”, Ann. Polon. Math. 102: 129–142.
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.
Wang, X.L.; Xu, H.Y.; Zhan T.S. (2014) “Properties of q-shift difference-differential polynomials of meromorphic functions”, Advances in Difference Equations 2014, Art. 249, pp.16.
Xu, H.Y. (2013) “On the value distribution and uniqueness of difference polynomials of meromorphic functions”, Advances in Difference Equations 2013, Art. 90, pp.15.
Yang, C.C. (1972) “On deficiencies of differential polynomials”, Math. Z. 125 (2): 107–112.
Yang, L. (1993) Value Distribution Theory. Springer-Verlag, Berlin.
Yi, H.X.; Yang, C.C. (2003) Uniqueness Theory of Meromorphic Functions. Kluwer Academic Publishers, Dordrecht; (1995) Chinese original: Science Press, Beijing.
Yi, H.X. (1999) “Meromorphic functions that share one or two values II”, Kodai Math. J. 22: 264–272.
Zhang, J.L. (2010) “Value distribution and shared sets of differences of meromorphic functions”, J. Math. Anal. Appl. 367(2): 401–408.
Comentarios
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-CompartirIgual 4.0.
Derechos de autor 2015 Hua Wang, Hong Yan Xu