ON THE UNIQUENESS OF PRODUCT OF DIFFERENCE POLYNOMIALS OF MEROMORPHIC FUNCTIONS

Abstract

In this paper, we study the uniqueness of product of difference polynomials $f^{n}[\prod_{j=1}^{d}f(z+c_{j})^{s_{j}}]^{(k)}$ and $g^{n}[\prod_{j=1}^{d}g(z+c_{j})^{s_{j}}]^{(k)}$, which are sharing a fixed point $z$ and $f$, $g$ share $\infty$ IM. The result extends the previous results of Cao and Zhang\cite{9} into product of difference polynomials.

Keywords

• Difference polynomials,Meromorphic functions,Product,Uniqueness

References

1. [1] Cao Y.H and Zhang X.B, Uniqueness of meromorphic functions sharing two values, J. Inequal. Appl. Vol:2012 (2012), 10 Pages.
2. [2] Dyavanal R.S and Desai R.V, Uniqueness of dierence polynomials of entire functions, Appl. J. Math. Vol:8 No.69 (2014), 3419-3424.
3. [3] Dyavanal R.S and Desai R.V, Uniqueness of q-shift difference and differential polynomials of entire functions, Far East J. Appl. Math. Vol:91 No.3 (2015), 189-202.
4. [4] Dyavanal R.S and Hattikal A.M, Uniqueness of difference-differential polynomials of entire functions sharing one value, Tamkang J. Math. Vol:47 No.2 (2016), 193-206.
5. [5] Dyavanal R.S and Hattikal A.M, Weighted sharing of uniqueness of difference polynomials of meromorphic functions, Far East J. Math. Sci. Vol:98 No.3 (2015), 293-313.
6. [6] Dyavanal R.S and Hattikal A.M, Unicity theorems on dierence polynomials of meromorphic functions sharing one value, Int. J. Pure Appl. Math. Sci. Vol:9 No.2 (2016), 89-97.
7. [7] Fang M.L and Yi H.X, Meromorphic functions that share xed-points, J. Math. Anal. Appl. Vol:268 No.2 (2002), 426-439.
8. [8] Hayman W.K Meromorphic functions, Claredon Press, Oxford, 1964.

9. [9] Wang X.L, Xu H.Y and Zhan T.S Properties of q-shift difference-differential polynomials of meromorphic functions, Adv. Diff. Equ. Vol:294 No.1 (2014),16 Pages.
10. [10] Xu X.Y, On the value distribution and dierence polynomials of meromorphic functions, Adv. Di. Equ. Vol:90 No.1 (2013), 13 Pages.
11. [11] Xu J.F, Lu F, Yi H.X, Fixed-points and uniqueness of meromorphic functions, Comp. Math. Appl. Vol:59 (2010), 9-17.
12. [12] Yang L, Value Distribution Theory, Springer-Verlag Berlin, 1993.
13. [13] Yang C.C, Hua H.X, Uniqueness and value sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math. Vol:22 (1997), 395-406.
14. [14] Yang C.C, Yi H.X, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht,2003; Chinese original: Science Press, Beijing, 1995.
15. [15] Zhang X.B, Further results on uniqueness of meromorphic functions concerning xed points, Abst. Appl. Anal. Article ID 256032 (2014), 7 Pages.