On the Hyers-Ulam Stability of the First-Order Difference Equation

الملخص EN

We prove Hyers-Ulam stability of the first-order difference equation of the form x i + 1 = F ( i , x i ) , where F is a given function with some moderate features.

Moreover, we introduce some conditions for the function F under which the difference equation is not stable in the sense of Hyers and Ulam.