Nonlinear Discrete Inequalities Method for the Ulam Stability of First Order Nonlinear Difference Equations

Abstract

In this paper, first we derive some nonlinear discrete inequalities, and then as an application, we study the Ulam stability of the first order nonlinear difference equation where f is a given function. The obtained result on Ulam stability is new to the literature in the sense that our approach does not require the explicit form of solutions of the investigated equation