Palabras clave
derivative
small function
función meromórfica
derivada
función pequeña
Cómo citar
Resumen
En este artículo, investigamos el problema de unicidad sobre una conjetura de R. Brück que concierne una función meromórfica que comparte un conjunto de pequeñas funciones con su derivada, y obtenemos algunos resultados que mejoran los teoremas dados por Zhang y Yang.
Citas
Al-Khaladi, A. (2005) “On meromorphic functions taht share one value with their derivative”, Analysis 25: 131–140.
Banerjee, A. (2007) “Weighted sharing of a small function by a meromorphic function and its derivative”, Comput. Math. Appl. 53: 1750–1761.
Brück, R. (1996) “On entire functions which share one value CM with their first derivative”, Results Math. 30: 21–24.
Chen, Z.-X.; Shon, K.H. (2004) “On conjecture of R. Brück concerning entire function sharing one value CM with its derivative”, Taiwanese J. Math. 8: 235–244.
Gundersen, G.G. (1980) “Meromorphic functions that share finite values with their derivative”, J. Math. Anal. Appl. 75: 441–446.
Gundersen, G.G.; Yang, L.-Z. (1998) “Entire functions that share one value with one or two of their derivatives”, J. Math. Anal. Appl. 223: 88–95.
Hayman, W.K. (1964) Meromorphic Functions. The Clarendon Press, Oxford.
Lin, W.-C.; Yi, H.-X. (2004) “Uniqueness theorems for meromorphic function”, Indian J. Pure Appl. Math. 35: 121–132.
Lahiri, I. (2001) “Weighted sharing and uniqueness of meromorphic functions”, Nagoya Math. J. 16(1): 193–206.
Lahiri, I. (2001) “Weighted value sharing and uniqueness of meromorphic functions”, Complex Var. Theory Appl. 46: 241–253.
Mues, E.; Steinmetz, N. (1986) “Meromorphe funktionen, die mit ihrer ersten und zweiten Ableitung einen endlichen Wert teilen”, Complex Var. Theory Appl. 6: 51–71.
Xu, H.-Y. (2007) “Uniqueness of transcendental meromorphic functions with their nonlinear differential polynomials sharing the small function”, Int. J. Math. Math. Sci. 2007, Article ID 84961, 14 pages.
Xu, H.-Y.; Cao, T.-B. (2009) “Uniqueness of entire or meromorphic functions sharing one value or a function with finite weight”, J. Inequal. Pure Appl. Math. 10, Art. 88.
Yang, L. (1993) Value Distribution Theory. Springer-Verlag, Berlin.
Yang, L.-Z.; Zhang, J.-L. (2008) “Non-existence of meromorphic solutions of Fermat type functional equation”, Aequationes Math. 76: 140–150.
Yi, H.-X.; Yang, C.-C. (1995/2003) Uniqueness Theory of Meromorphic Functions. Science Press/Kluwer Academic Publishers, Beijing/New York.
Yi, H.-X. (1999) “Meromorphic functions that share one or two values II”, Kodai Math. J. 22: 264–272.
Yi, H.-X. (1997) “Unicity theorems for meromorphic functions whose n-th derivatives share the same 1-points”, Complex Var. Theory Appl. 34: 421–436.
Zhang, Q.-C. (2005) “Meromorphic function that shares one small function with its derivative”, J. Inequal. Pure Appl. Math. 6, Art. 116.
Zhang, J.-L.; Yang, L.-Z. (2009) “A power of a meromorphic function sharing a small function with its derivative”, Ann. Acad. Sci. Fenn. Math. 34: 249–260.
Zhang, J.-L.; Yang, L.-Z. (2007) “Some results related to a conjecture of R. Brück”, J. Inequal. Pure Appl. Math. 8, Art. 18.
Zheng, J.-H.; Wang, S.-P. (1992) “On uncity properties of meromorphic functions and their derivatives”, Adv. in Math. (in Chinese) 21: 334–341.