Results on uniqueness of entire functions whose certain difference polynomials share a small function

A. Banerjee and S. Mukherjee, Uniqueness of meromorphic functions concerning differential monomials sharing the same value, Bull. Math. Soc. Sci. Math. Roumanie (N. S.), 50(2007), 191–206. M. R. Chen and Z. X. Chen, Properties of difference polynomials of entire functions with finite order, Chinese Ann. Math., 33(2012), 359–374. Y. M. Chiang and S. J. Feng, On the Nevanlinna characteristic of f(z + η) and difference equations in the complex plane, Ramanujan J., 16(2008), 105–129. M. L. Fang and X. H. Hua, Entire functions that share one value, Nanjing Daxue Xuebao Shuxue Bannian Kan, 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 derivative with application to difference equations, J. Math. Anal. Appl., 314(2006), 477–487. W. K. Hayman, Meromorphic Functions, Clarendon Press (Oxford, 1964). I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46(2001), 241–253. I. Lahiri, Value distribution of certain differential polynomials, Int. J. Math. Math. Sci., 28(2001), 83–91. I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter deGruyter (Berlin–New York, 1993). I. Laine and C. C. Yang, Value distribution of difference polynomials, Proc. Japan Acad. Ser. A Math. Sci., 83(2007), 148–151. S. H. Lin and W. C. Lin, Uniqueness of meromorphic functions concerning weakly weighted sharing, Kodai Math. J., 29(2006), 269–280. X. Q. Lin and W. C. Lin, Uniqueness of entire functions sharing one value, Acta Math. Sci. Ser. B Engl. Ed., 31(2011), 1062–1076. W. C. Lin and H. X. Yi, Uniqueness theorems for meromorphic functions concerning fixed points, Complex Var. Theory Appl., 49(2004), 793–806. C. Meng, Uniqueness of entire functions concerning difference polynomials, Math. Bohem., 139(2014), 89–97. X. G. Qi, L. Z. Yang, and K. Liu, Uniqueness and periodicity of meromorphic functions concerning the difference operator, Comput. Math. Appl., 60(2010), 1739–1746. P. Sahoo, Uniqueness of entire functions related to difference polynomials, Commun. Math. Stat. 3(2015), 227–238. P. Sahoo and S. Seikh, Meromorphic functions whose certain differential polynomials share a small function with finite weight, Analysis (Munich), 33(2013), 143–157. H. Y. Xu, T. B. Cao, and S. Liu, Uniqueness results of meromorphic functions whose nonlinear differential 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. C. C. Yang and X. H. Hua, Uniqueness and value sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math., 22(1997), 395–406. C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer (Dordrecht, 2003). 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.