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Revista de Matemática Teoría y Aplicaciones
Print version ISSN 1409-2433
Rev. Mat vol.23 n.1 San José Jan./Jun. 2016
Artículos
On a conjecture of R. Brück concerning meromorphic function sharing small functions
Sobre una conjetura de R.Brück concerniente a la función meromórfica que comparte pequeñas funciones
1Department of Informatics and Engineering, Jingdezhen Ceramic Institute, Jingdezhen,Jiangxi, 333403, China. E-Mail: xhyhhh@126.com
2Institute of Mathematics and informatics, Jiangxi Normal University, Nanchang, Jiangxi,330022, China. E-Mail: yicaifeng55@163.com
3Department of Informatics and Engineering, Jingdezhen Ceramic Institute, Jingdezhen, Jiangxi, 333403, China. E-Mail: hhhlucy2012@126.com
In this paper, we investigate the uniqueness problem on a conjecture of R. Brück concerning meromorphic function sharing the set of small functions with its derivative, and obtain some results which improve the theorems given by Zhang and Yang.
Keywords: meromorphic function; derivative; small function
En este artículo, nvestigamos 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.
Palabras clave: función meromórfica; derivada; función pequeña
REFERENCES
Al-Khaladi, A.(2005) "On meromorphic functions taht share one value with their derivative", Analysis 25: 131-140. [ Links ]
Banerjee, A. (2007) "Weighted sharing of a small function by a meromorphic function and its derivative", Comput. Math. Appl53: 1750-1761. [ Links ]
Brück, R.(1996) "On entire functions which share one value CM with their first derivative", Results Math30: 21-24. [ Links ]
Chen, Z.-X.; Shon, K.H.(2004) "On conjecture of R. Brück concerning entire function sharing one value CM with its derivative", Taiwanese J. Math8: 235-244. [ Links ]
Gundersen, G.G.(1980) "Meromorphic functions that share finite values with their derivative", J. Math. Anal. Appl75: 441-446. [ Links ]
Gundersen, G.G.; Yang, L.-Z.(1998) "Entire functions that share one value with one or two of their derivatives", J. Math. Anal. Appl223: 88-95. [ Links ]
Hayman, W.K.(1964) Meromorphic Functions. The Clarendon Press, Oxford. [ Links ]
Lin, W.-C.; Yi, H.-X.(2004) "Uniqueness theorems for meromorphic function", Indian J. Pure Appl. Math35: 121-132. [ Links ]
Lahiri, I.(2001) "Weighted sharing and uniqueness of meromorphic functions", Nagoya Math. J16(1): 193-206. [ Links ]
Lahiri, I.(2001) "Weighted value sharing and uniqueness of meromorphic functions", Complex Var. Theory Appl46: 241-253. [ Links ]
Mues, E.; Steinmetz, N.(1986) "Meromorphefunktionen, die mitihrerersten und zweitenAbleitungeinenendlichen Wert teilen", Complex Var. Theory Appl6: 51-71. [ Links ]
Xu, H.-Y.(2007) "Uniqueness of transcendental meromorphic functions with their nonlinear differential polynomials sharing the small function", Int. J. Math. Math. Sci2007, Article ID 84961, 14 pages. [ Links ]
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. Math10, Art. 88. [ Links ]
Yang, L.(1993) Value Distribution Theory. Springer-Verlag, Berlin. [ Links ]
Yang, L.-Z.; Zhang, J.-L.(2008) "Non-existence of meromorphic solutions of Fermat type functional equation", Aequationes Math76: 140- 150. [ Links ]
Yi, H.-X.; Yang, C.-C.(1995/2003) Uniqueness Theory of Meromorphic Functions. Science Press/Kluwer Academic Publishers, Beijing/New York. [ Links ]
Yi, H.-X. (1999) "Meromorphic functions that share one or two values II", Kodai Math. J22: 264-272. [ Links ]
Yi, H.-X.(1997) "Unicity theorems for meromorphic functions whose nth derivatives share the same 1-points", Complex Var. Theory Appl34: 421-436. [ Links ]
Zhang, Q.-C.(2005) "Meromorphic function that shares one small function with its derivative", J. Inequal. Pure Appl. Math6, Art. 116. [ Links ]
Zhang, J.-L.; Yang, L.-Z.(2009) "A power of a meromorphic function sharing a small function with its derivative", Ann. Acad. Sci. Fenn. Math34: 249-260. [ Links ]
Zhang, J.-L.; Yang, L.-Z.(2007) "Some results related to a conjecture of R. Brück", J. Inequal. Pure Appl. Math8, Art. 18. [ Links ]
Zheng, J.-H.; Wang, S.-P. (1992) "On uncity properties of meromorphic functions and their derivatives", Adv. in Math.(in Chinese) 21: 334-341. [ Links ]
Received: April 27, 2015; Revised: September 02, 2015; Accepted: October 19, 2015
This is an open-access article distributed under the terms of the Creative Commons Attribution License
