On the Hyers-Ulam Stability of the First-Order Difference Equation - Soon-Mo Jung; Young Woo Nam (Journal of Function Spaces)
We prove Hyers-Ulam stability of the first-order difference equation of the form xi+1=F(i,xi), 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.