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.
Highlights
Ulam [1] proposed the well-known Ulam stability problem. The difficulty of this problem lies in the conditions to be imposed to guarantee the existence of a linear mapping near an approximately linear mapping
It is crucial to find error bounds to the approximations when replacing the exact solutions in practical problems
For all x ∈ [ a, b], we say that the given problem (1) and (2) has the Hyers–Ulam–Rassias stability
Summary
The study of problems involving differential, functional, integro-differential and integral equations, in particular their stability issues, has suffered greatly from the growing engagement over the years with a spread of interest among researchers, for example, see [2,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27] Their applicability in mathematical models for which we cannot find exact solutions, namely those involving symmetry issues, the study of the stability of the approximate solutions is an open field of research. Of Newtonian and non-Newtonian fluids related to one-dimensional models obtained by Cosserat Theory associated with fluid dynamics (see [28,29])
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