Hyers-Ulam and Hyers-Ulam-Rassias Stability for a Class of Integro-Differential Equations

Castro, L. P.; Simões, A. M.

doi:10.1007/978-3-319-91065-9_3

Cited by 9 publications

(8 citation statements)

References 25 publications

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“…Among those, we point out functional equations, differential equations and integral equations. This is also connected with the applicability of those equations in different areas of the knowledge like chemical reactions, diffraction theory, elasticity, fluid flow, heat conduction, and population dynamics (cf other works).…”

Section: Introductionmentioning

confidence: 91%

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

Castro

Simões

2018

Math Methods in App Sciences

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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.

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Section: Introductionmentioning

confidence: 91%

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

Castro

Simões

2018

Math Methods in App Sciences

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“…In general, to study the stability of functional, integral and integro-differential equations, it is usual to consider fixed point arguments, for example, see [18,[31][32][33][34][35][36][37][38]. Here, we consider the Banach fixed point theorem, which we recall next.…”

Section: Notations and Preliminariesmentioning

confidence: 99%

New Sufficient Conditions to Ulam Stabilities for a Class of Higher Order Integro-Differential Equations

2021

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In this work, we present sufficient conditions in order to establish different types of Ulam stabilities for a class of higher order integro-differential equations. In particular, we consider a new kind of stability, the σ-semi-Hyers-Ulam stability, which is in some sense between the Hyers–Ulam and the Hyers–Ulam–Rassias stabilities. These new sufficient conditions result from the application of the Banach Fixed Point Theorem, and by applying a specific generalization of the Bielecki metric.

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“…To study the stability of functional, integral, and integro-differential equations, some of the usual techniques are a combination of fixed-point results with a generalized metric in appropriate contexts; for example, see earlier studies. [17][18][19][20][21]24,26,27 So we will recall the definition of generalized metric, and the Banach fixed-point theorem which we will see plays a very important role in obtaining our results. Definition 4 ( 28 ).…”

Section: Introductionmentioning

confidence: 99%

Different stabilities for oscillatory Volterra integral equations

Simões

2023

Math Methods in App Sciences

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Inspired by the increasing development of theories subordinate to the topic of stability in the sense of Ulam–Hyers and Ulam–Hyers–Rassias, we present in this paper new sufficient conditions for concluding the stability of classes of integral equations with kernels depending on sine and cosine functions. This will be done by taking the profit of fixed‐point arguments in the framework of spaces of continuous functions endowed with a generalization of the Bielecki metric. After presenting the main theorems, some examples are provided to verify the effectiveness of the proposed theoretical results.

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Hyers-Ulam and Hyers-Ulam-Rassias Stability for a Class of Integro-Differential Equations

Cited by 9 publications

References 25 publications

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

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

New Sufficient Conditions to Ulam Stabilities for a Class of Higher Order Integro-Differential Equations

Different stabilities for oscillatory Volterra integral equations

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