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- Hyers-Ulam and Hyers-Ulam-Rassias stability of a class of Hammerstein integral equationsPublication . Simões, A. M.; Castro, L. P.The purpose of this paper is to study different kinds of stability for a class of Hammerstein integral equations. Sufficient conditions are derived in view to obtain Hyers-Ulam stability and Hyers-Ulam-Rassias stability for such a class of Hammerstein integral equations. The consequent different cases of a finite interval and an infinite interval are considered, and some concrete examples are included to illustrate the results.
- Hyers-Ulam and Hyers-Ulam-Rassias stability of a class of integral equations on finite intervalsPublication . Simões, A. M.; Castro, L. P.The purpose of this work is to study different kinds of stability for a class of integral equations defined on a finite interval. Sufficient conditions are derived in view to obtain Hyers-Ulam stability and Hyers-Ulam-Rassias stability by using fixed point techniques and the Bielecki metric.
- A Hyers-Ulam stability analysis for classes of Bessel equationsPublication . Castro, L. P.; Simões, A. M.Mathematical modeling helps us to better understand different natural phenomena. Modeling is most of the times based on the consideration of appropriate equations (or systems of equations). Here, differential equations are well-known to be very useful instruments when building mathematical models { specially because that the use of derivatives offers several interpretations associated with real life laws. Differential equations are classi ed based on several characteristics and, in this way, allow different possibilities of building models. In this paper we will be concentrated in analysing certain stability properties of classes of Bessel differential equations. In fact, the main aim of this work is to seek adequate conditions to derive different kinds of stabilities for the Bessel equation and for the modi ed Bessel equation by considering a perturbation of the trivial solution. In this way, suficient conditions are obtained in order to guarantee Hyers-Ulam-Rassias, sigma-semi-Hyers-Ulam and Hyers-Ulam stabilities for those equations.
- Different Types of Hyers-Ulam-Rassias Stabilities for a Class of Integro-Differential EquationsPublication . Simões, A. M.; Castro, L. P.We study different kinds of stabilities for a class of very general nonlinear integro-differential equations involving a function which depends on the solutions of the integro-differential equations and on an integral of Volterra type. In particular, we will introduce the notion of {\it semi-Hyers-Ulam-Rassias stability}, which is a type of stability somehow in-between the Hyers-Ulam and Hyers-Ulam-Rassias stabilities. This is considered in a framework of appropriate metric spaces in which sufficient conditions are obtained in view to guarantee Hyers-Ulam-Rassias, semi-Hyers-Ulam-Rassias and Hyers-Ulam stabilities for such a class of integro-differential equations. We will consider the different situations of having the integrals defined on finite and infinite intervals. Among the used techniques, we have fixed point arguments and generalizations of the Bielecki metric. Examples of the application of the proposed theory are included.