In this paper, we investigate the distribution of zeros as well as the uniqueness problems of certain type of differential polynomials sharing a small function with finite weight. The result obtained improves and generalizes the recent results.
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 A. Banerjee, Meromorphic functions sharing one value, Int. J. Math. Math. Sci., 22(2005), 3587-3598.
 S. S. Bhoosnurmath and S. R. Kabbur, Value distribution and uniqueness theorems for difference of entire and meromorphic functions, Int. J. Anal. Appl., 2(2013), 124-136.
 M. R. Chen and Z. X. Chen, Properties of difference polynomials of entire functions with Finite order, Chinese Ann. Math. Ser. A, 33(2012), 359-374.
 Y. M. Chiang and S. J. Feng, On the Nevanlinna characteristic of f(z + ɳ) and difference equations in the complex plane, Ramanujan J., 16(2008), 105-129.
 M. L. Fang and W. Hong, A unicity theorem for entire functions concerning dif ferential poly- nomials, Indian J. Pure Appl. Math., 32(2001), 1343-1348.
 M. L. Fang and X. H. Hua, Entire functions that share one value, J. Nanjing Univ. Math. Biquarterly, 13(1996), 44-48.
 R. G. Halburd and R. J. Korhonen, Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math., 31(2006), 463-478.
 R. G. Halburd and R. J. Korhonen, Difference analogue of the lemma on the logarithmic deriva- tive with application to difference equations, J. Math. Anal. Appl., 314(2006), 477-487.
 W. K. Hayman, Meromorphic Functions. Oxford Mathematical Monographs Clarendon Press, Oxford 1964.
 I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46(2001), 241-253.
 I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin/Newyork, 1993.
 I. Laine and C. C. Yang, Value distribution of difference polynomials, Proc. Japan Acad. SerA Math. Sci., 83(2007), 148-151.
 X. Luo and W. C. Lin, Value sharing results for shifts of meromorphic functions, J. Math. Anal. Appl., 377(2011), 441-449.
 X. G. Qi, L. Z. Yang and K. Liu, Uniqueness and periodicity of meromorphic functions con- cerning the difference operator, Comput. Math. Appl., 60(2010), 1739-1746.
 P. Sahoo, Uniqueness and weighted sharing of entire functions, Kyungpook Math. J.,51(2011), 145-164.
 P. Sahoo, Entire functions that share fixed points with nite weights, Bull. Belgian Math. Soc.-Simon Stevin, 18(2011), 883-895.
 C. C. Yang and X. H. Hua, Uniqueness and value sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math., 22(1997), 395-406.
 H. X. Yi and C. C. Yang, Uniqueness Theory of Meromorphic Functions, Science Press, Beijing, 1995.
 J. L. Zhang, Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl., 367(2010), 401-408.
 J. L. Zhang and L. Z. Yang, Some results related to a conjecture of R. Bruck, J. Inequal. Pure Appl. Math., 8(2007), Art. 18.
 P. Sahoo and B. Saha, Value distribution and uniqueness of certain type of difference polyno- mials, App. Math. E-Notes, 16(2016), 33-34.
 P. Sahoo and S. Seikh, Meromorphic functions whose certain differential polynomials share a small function with finite weight, Analysis(Munich), 33(2013), 143-157.
 W.C. Lin and H.X. Yi, Uniqueness theorems for meromorphic functions concerning fixed points, Complex Var. Theory Appl. 49(2004), 793-806.
 H.Y. Xu, T.B. Cao, and S. Liu, Uniqueness of meromorphic functions whose nonlinear differ- ential polynomials have one nonzero pseudo value, Mat.Vesnik, 64(2012), 1-16.
 H. Y. Xu, C. F. Yi and T.B. Cao, Uniqueness of meromorphic functions and differential polynomials sharing one value with finite weight, Ann. Polon. Math, 95(2009), 55-66.
 I. Lahiri, Value distribution of certain differential polynomials, Int. J. Math. Math. Sci., 28(2001), 83-91.