ON THE UNIQUENESS PROBLEMS OF ENTIRE FUNCTIONS AND THEIR DIFFERENCE OPERATORS

Abstract

In this paper, the uniqueness problems of entire functions and their difference operators are investigated. It is shown that if a finite order entire function $f$ shares $0,\alpha$ CM with its difference operator $\Delta_\eta f(z)=f(z+\eta)-f(z)$, then $\Delta_\eta f\equiv f$, where $\alpha$ is an entire function with order less than $f$. The research results also include a difference analogue of Brück conjecture, and extend some results in Chen-Yi Results Math., 63 (2013), 557-565).