Uniqueness of Entire Functions Related to Difference Polynomials

Abstract

With the notion of weakly weighted sharing and relaxed weighted sharing, we investigate the uniqueness problems of certain type of difference polynomials sharing a small function. The results of the paper extend and generalize some recent results due to Meng (Math. Bohem. 139:89–97, 2014).

Keywords

Uniqueness / Entire function / Difference polynomial

References

[1] Banerjee A, Mukherjee S. Uniqueness of meromorphic functions concerning differential monomials sharing the same value. Bull. Math. Soc. Sci. Math. Roum. Nouv. Ser.. 2007, 50 191-206

[2] Bhoosnurmath SS, Kabbur SR. Value distribution and uniqueness theorems for difference of entire and meromorphic functions. Int. J. Anal. Appl.. 2013, 2 124-136

[3] Chen MR, Chen ZX. Properties of difference polynomials of entire functions with finite order. Chin. Ann. Math.. 2012, 33 359-374

[4] Chiang YM, Feng SJ. On the Nevanlinna characteristic of $f(z+\eta )$ and difference equations in the complex plane. Ramanujan J.. 2008, 16 105-129

[5] Fang CY, Fang ML. Uniqueness of meromorphic functions and differential polynomials. Comput. Math. Appl.. 2002, 44 607-617

[6] Hayman WK. Picard values of meromorphic Functions and their derivatives. Ann. Math.. 1959, 70 9-42

[7] Hayman WK. Meromorphic Functions. 1964 Oxford: The Clarendon Press

[8] Lahiri I. Value distribution of certain differential polynomials. Int. J. Math. Math. Sci.. 2001, 28 83-91

[9] Lahiri I. Weighted value sharing and uniqueness of meromorphic functions. Complex Var. Theory Appl.. 2001, 46 241-253

[10] Laine I. Nevanlinna Theory and Complex Differential Equations. 1993 Berlin/Newyork: Walter de Gruyter

[11] Lin SH, Lin WC. Uniqueness of meromorphic functions concerning weakly weighted sharing. Kodai Math. J.. 2006, 29 269-280

[12] Lin WC, Yi HX. Uniqueness theorems for meromorphic functions concerning fixed points. Complex Var. Theory Appl.. 2004, 49 793-806

[13] Lin XQ, Lin WC. Uniqueness of entire functions sharing one value. Acta Math. Sci., Ser. B. Engl. Ed.. 2011, 31 1062-1076

[14] Luo X, Lin WC. Value sharing results for shifts of meromorphic functions. J. Math. Anal. Appl.. 2011, 377 441-449

[15] Meng C. Uniqueness of entire functions concerning difference polynomials. Math. Bohem.. 2014, 139 89-97

[16] Yang CC, Hua XH. Uniqueness and value sharing of meromorphic functions. Ann. Acad. Sci. Fenn. Math.. 1997, 22 395-406

[17] Yi HX. Meromorphic functions that share one or two values. Complex Var. Theory Appl.. 1995, 28 1-11

[18] Yi HX, Yang CC. Uniqueness Theory of Meromorphic Functions. 1995 Beijing: Science Press

[19] Zhang JL. Value distribution and shared sets of differences of meromorphic functions. J. Math. Anal. Appl.. 2010, 367 401-408