On a conjecture of R. Brück concerning meromorphic function sharing small functions

• Autores: Hong Yan, Cai Feng Yi, Hua Wang
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 23, Nº. 1, 2016, págs. 291-308
• Idioma: inglés
• DOI: 10.15517/rmta.v23i1.22555
• Títulos paralelos:
  • Sobre una conjetura de R. Brück concerniente a la función meromórfica que comparte pequeñas funciones
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• Resumen
  • español

    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.

  • English

    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.

• Referencias bibliográficas
  • 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...
  • 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:...
  • 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....
  • Xu, H.-Y. (2007) “Uniqueness of transcendental meromorphic functions with their nonlinear differential polynomials sharing the small function”,...
  • Xu, H.-Y.; Cao, T.-B. (2009) “Uniqueness of entire or meromorphic functions sharing one value or a function with finite weight”, J. Inequal....
  • 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:...
  • 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....
  • 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.