A result concerning the stability of some difference equations and its applications (Q1857386)

The author investigates the stability problem in the sense of Hyers-Ulam for the following difference equation \[ f(x+p,y+q)-\varphi (x,y) f(x,y)-g(x,y)=0, \] where \(f,g:\mathbb N\times \mathbb N \rightarrow \mathbb R\) and \(\varphi \) satisfy the inequality \[ |f(x+p,y+q)-\varphi (x,y) f(x,y)-g(x,y)|\leq \delta\quad (\delta >0) \] for all \(x,y\in \mathbb N\) and \(p,q\in \mathbb N\) be fixed, and \(\mathbb N\) denotes the set of all positive integers.