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 sigma-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.