| Name: | Description: | Size: | Format: | |
|---|---|---|---|---|
| 176.94 KB | Adobe PDF |
Authors
Advisor(s)
Abstract(s)
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.
Description
Keywords
Hyers-Ulam stability Semi-Hyers-Ulam-Rassias stability Hyers-Ulam-Rassias stability Banach fixed point theorem Integro-differential equation
Citation
L. P. Castro, A. M. Simões, Different Types of Hyers-Ulam-Rassias Stabilities for a Class of Integro-Differential Equations, Filomat 31:17 (2017), 5379–5390.
Publisher
Faculty of Sciences and Mathematics, University of Nis, Serbia