Mathematica Bohemica, Vol. 141, No. 1, pp. 13-36, 2016
Nonlinear differential polynomials sharing a non-zero polynomial with finite weight
Abhijit Banerjee, Molla Basir Ahamed
Abstract: In the paper, dealing with a question of Lahiri (1999), we study the uniqueness of meromorphic functions in the case when two certain types of nonlinear differential polynomials, which are the derivatives of some typical linear expression, namely $h^n(h-1)^m$ ($h=f,g$), share a non-zero polynomial with finite weight. The results obtained in the paper improve, extend, supplement and generalize some recent results due to Sahoo (2013), Li and Gao (2010). In particular, we have shown that under a suitable choice of the sharing non-zero polynomial or when the first derivative is taken under consideration, better conclusions can be obtained.
Affiliations: Abhijit Banerjee, Department of Mathematics, University of Kalyani, Kalyani, Nadia, West Bengal 741235, India, e-mail: abanerjee_kal@yahoo.co.in, abanerjee_kal@rediffmail.com; Molla Basir Ahamed, Department of Mathematics, Kalipada Ghosh Tarai Mahavidyalaya, Bagdogra, Darjeeling, West Bengal 734014, India, e-mail: bsrhmd116@gmail.com, bsrhmd117@gmail.com
