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Title: Different types of Hyers-Ulam-Rassias stabilities for a class of integro-differential equations
Author: Castro, L. P.
Simões, A. M.
Keywords: Hyers-Ulam stability
Semi-Hyers-Ulam-Rassias stability
Hyers-Ulam-Rassias stability
Banach fixed point theorem
Integro-differential equation
Issue Date: 30-Nov-2017
Publisher: Faculty of Sciences and Mathematics, University of Nis, Serbia
Abstract: 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.
Peer review: yes
DOI: 10.2298/FIL1717379C
ISSN: 2406-0933
Appears in Collections:CIDMA - Artigos
FAAG - Artigos

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