Entire functions sharing a finite set with their difference operators (Q428963)

The author proves a result concerning the growth of solutions of a certain difference equation. He also obtains a uniqueness result on entire functions sharing a set with their difference operators, where the set consists of two entire functions of smaller orders. The author also proves a uniqueness result for entire functions sharing a finite set with their difference operators. The results obtained in this article are related with the articles [\textit{K. Liu}, J. Math. Anal. Appl. 359, No. 1, 384--393 (2009; Zbl 1177.30035)] and [\textit{Q. C. Zhang}, Indian J. Pure Appl. Math. 30, No. 7, 667--682 (1999; Zbl 0934.30025)].