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

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 a...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2018-11, Vol.41 (17), p.7367-7383
Main Authors: Castro, L. P., Simões, A. M.
Format: Article
Language:English
Subjects:
Banach fixed point theorem
Bielecki metric
Domains
Estimating techniques
Hyers‐Ulam stability
Hyers‐Ulam‐Rassias stability
Integral equations
Mathematical analysis
Nonlinear equations
nonlinear integral equation
Stability analysis
σ‐semi‐Hyers‐Ulam stability
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Summary: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.4857