ABHIJIT BANERJEE AND SANJAY MALLICK

Yıl 2016, Cilt: 65 Sayı: 1, 71 - 86, 01.02.2016

Abhijit Banerjee Sanjay Mallıck

https://doi.org/10.1501/Commua1_0000000745

Cited By: 1

Öz

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

Anahtar Kelimeler

Meromorphic function, derivative, small function, uniqueness, 30D35

Kaynakça

• 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.