Hyers‐Ulam‐Rassias stability of nonlinear integral equations through the Bielecki metric

descriptionPublicationkeyboard_double_arrow_right Article 20 Apr 2018 Portugal English Publisher:WileyJournal:Mathematical Methods in the Applied Sciences, volume 41, pages 7,367-7,383 (issn: 0170-4214, eissn: 1099-1476,

Copyright policy )Funded by:FCT | Center for Research and D..., FCT | Center of Mathematics and...

Authors: Simões, A. M.; Castro, L. P.;

doi: 10.1002/mma.4857

handle: 10773/22992 , 10400.6/4747

Hyers‐Ulam‐Rassias stability of nonlinear integral equations through the Bielecki metric

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Abstract

We analyse different kinds of stabilities for classes of nonlinear integral equations of Fredholm and Volterra type. Sufficient conditions are obtained in order to guarantee Hyers‐Ulam‐Rassias, σ‐semi‐Hyers‐Ulam and Hyers‐Ulam stabilities for those integral equations. Finite and infinite intervals are considered as integration domains. Those sufficient conditions are obtained based on the use of fixed point arguments within the framework of the Bielecki metric and its generalizations. The results are illustrated by concrete examples.

Country

Portugal

Related Organizations

University of Aveiro
Portugal
NOVAMath Center for Mathematics and Applications
Portugal
University of Aveiro
Portugal
University of Beira Interior
Portugal

Keywords

Sigma-semi-Hyers-Ulam stability, Stability theory of functional-differential equations, Banach fixed point theorem, \(\sigma\)-semi-Hyers-Ulam stability, Volterra integral equations, Stability theory for integral equations, σ‐semi‐Hyers‐Ulam stability, Nonlinear integral equation, nonlinear integral equation, Hyers‐Ulam‐Rassias stability, Hyers‐Ulam stability, Bielecki matric, Fixed-point theorems, Banach fixed point theorem;, Hyers-Ulam stability, Hyers-Ulam-Rassias stability, Bielecki metric

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