ABHIJIT BANERJEE AND SANJAY MALLICK
Year 2016,
Volume: 65 Issue: 1, 71 - 86, 01.02.2016
Abhijit Banerjee
Sanjay Mallıck
Abstract
The purpose of the paper is to obtain some su¢ cient conditions forwhich two differential polynomials sharing a small function satisfies conclusionsof Brück [3] conjecture. The result present in the paper will unify, improve andgeneralize several existing results. We have exhibited a number of examples toshow that some conditions used in the paper are essential. In the concludingpart of the paper we propose two open problems for further investigations
References
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- L. A. Rubel and C. C. Yang, Values shared by an entire function and its derivative, Com- plex analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976), Lecture Notes in Math., (1977), 101-103, Springer, Berlin.
- L. Z. Yang, Solution of a diğ erential equation and its applications, Kodai Math. J., 22(1999), 464.
- H. X. Yi, On characteristic function of a meromorphic function and its derivative, Indian J. Math., 33(2)(1991), 119-133.
- Q. C. Zhang, The uniqueness of meromorphic functions with their derivatives, Kodai Math. J., 21(1998), 179-184.
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- T. D. Zhang and W.R. Lü, Notes on meromorphic function sharing one small function with its derivative, Complex Var. Ellip. Eqn., 53(9)(2008), 857-867.
- Current address : Department of Mathematics, University of Kalyani, West Bengal 741235, India.
Year 2016,
Volume: 65 Issue: 1, 71 - 86, 01.02.2016
Abhijit Banerjee
Sanjay Mallıck
References
- T. C. Alzahary and H. X. Yi, Weighted value sharing and a question of I.Lahiri, Complex Var. Theory Appl., 49(15) (2004), 1063-1078.
- A. Banerjee, Meromorphic functions sharing one value, Int. J. Math. Math. Sci., 22(2005), 3598.
- R. Brück, On entire functions which share one value CM with their …rst derivative, Results Math., 30(1996), 21-24.
- C. T. Chuang, On diğ erential polynomials, Analysis of one complex variable, (Laramie, Wyo., ), 12-32, World Sci. Publishing Singapore, (1987).
- W. Doeringer, Exceptional values of diğ erential polynomials, Paci…c J. Math., 98(1)(1982), 62.
- G. G. Gundersen and L. Z. Yang, Entire functions that share one value with one or two of their derivatives, J. Math. Anal. Appl., 223(1)(1998), 88-95.
- W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, (1964).
- I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., (2001), 193-206.
- I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46(2001), 241-253.
- I. Lahiri and A. Banerjee, Weighted sharing of two sets, Kyungpook Math. J., 46(1)(2006), 87.
- I. Lahiri and S. Dewan, Value distribution of the product of a meromorphic function and its derivative, Kodai Math. J., (2003), 95-100.
- I. Lahiri and A. Sarkar, Uniqueness of meromorphic function and its derivative, J. Inequal. Pure Appl. Math., 5(1)(2004), Art.20 [ONLINE http://jipam.vu.edu.au/].
- L. Liu, Uniqueness of meromorphic functions that share one small function with their deriv- atives, J.Math. Sci. : Adv. Appl., 6(2)(2010), 241-255.
- N. Li and L. Z. Yang, Meromorphic function that shares one small function with its diğ er- ential polynomial, Kyungpook Math. J., 50(2010), 447-454.
- A. Z. Mohon’ko, On the Nevanlinna characteristics of some meromorphic functions, Theory of Functions, Functional Analysis and Their Applications, 14(1971), 83-87.
- E. Mues and N. Steinmetz, Meromorphe funktionen die unit ihrer ableitung werte teilen, Manuscripta Math., 29(1979) 195-206.
- L. A. Rubel and C. C. Yang, Values shared by an entire function and its derivative, Com- plex analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976), Lecture Notes in Math., (1977), 101-103, Springer, Berlin.
- L. Z. Yang, Solution of a diğ erential equation and its applications, Kodai Math. J., 22(1999), 464.
- H. X. Yi, On characteristic function of a meromorphic function and its derivative, Indian J. Math., 33(2)(1991), 119-133.
- Q. C. Zhang, The uniqueness of meromorphic functions with their derivatives, Kodai Math. J., 21(1998), 179-184.
- Q. C. Zhang, Meromorphic function that shares one small function with its derivative. J. Inequal. Pure Appl. Math., 6(4)(2005), Art.116 [ ONLINE http://jipam.vu.edu.au/].
- T. D. Zhang and W.R. Lü, Notes on meromorphic function sharing one small function with its derivative, Complex Var. Ellip. Eqn., 53(9)(2008), 857-867.
- Current address : Department of Mathematics, University of Kalyani, West Bengal 741235, India.