New Sufficient Conditions to Ulam Stabilities for a Class of Higher Order Integro-Differential Equations

Abstract

In this work, we present sufficient conditions in order to establish different types of Ulam stabilities for a class of higher order integro-differential equations. In particular, we consider a new kind of stability, the σ-semi-Hyers-Ulam stability, which is in some sense between the Hyers–Ulam and the Hyers–Ulam–Rassias stabilities. These new sufficient conditions result from the application of the Banach Fixed Point Theorem, and by applying a specific generalization of the Bielecki metric.

Keywords

• Hyers–Ulam stability
• Hyers–Ulam–Rassias stability
• Banach fixed point theorem