Abstract
In this paper we deal with the uniqueness of meromorphic functions when two nonlinear differential polynomials generated by two meromorphic functions share a small function. We consider the case for some general differential polynomials [fnP(f)f,] where P(f) is a polynomial which generalize some result due to Abhijit Banerjee and Sonali Mukherjee [1].
Highlights
In this paper, we use the standard notations and terms in the value distribution theory [2]
In this paper we deal with the uniqueness of meromorphic functions when two nonlinear differential polynomials generated by two meromorphic functions share a small function
We consider the case for some general differential polynomials [ f nP( f ) f ] where P(f) is a polynomial which generalize some result due to Abhijit Banerjee and Sonali Mukherjee [1]
Summary
We use the standard notations and terms in the value distribution theory [2]. We denote by Nk) r, f the counting function for poles of f(z) with multiplicities k, and by Nk) r, f the corresponding one for which the multiplicity is not counted. Let f and g be two nonconstant meromorphic functions and n( 13) be an integer. Lin-Yi [5] proved the following result. Let f and g be two transcendental meromorphic functions and n( 13) be an integer. With the notion of weighted sharing of value recently the first author [6] improved Theorem A as follows. In the mean time Lahiri and Sarkar [7] studied the uniqueness of meromorphic functions corresponding to nonlinear differential polynomials which are different from that of previously mentioned and proved the following. If [ f n P( f ) f ] and [ gn P(g)g ] share “ , 2 ” f g
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