Hyers–Ulam stability of the iterative equation with a general boundary restriction

Xia, Chao

doi:10.1016/j.cam.2017.03.024

Cited by 4 publications

(4 citation statements)

References 20 publications

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“…for all t ∈ I, where ϕ : I → (0, ∞) is a nondecreasing continuous function, then there exists a unique solution y 0 : I → R of Volterra integral equation (2) satisfying (7) for all t ∈ I, where η is an arbitrary fixed real number with η > L.…”

Section: Resultsmentioning

confidence: 99%

“…After this result of Hyers, a new concept of stability for functional equations established, called today Hyers-Ulam stability, and many papers devoted to this subject (see for example [3,4,5,6,7,8,9]). In 1978, T. Rassias [10] provided a remarkable generalization with the following well-known result, which known as Hyers-Ulam-Rassias stability today.…”

Section: Introductionmentioning

confidence: 99%

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On the Ulam Type Stability of Nonlinear Volterra Integral Equations

Öğrekçi¹,

Başcı²,

Mısır³

2021

Preprint

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Ulam Type Stability of Nonlinear Volterra Integral Equations

Öğrekçi¹,

Başcı²,

Mısır³

2021

Preprint

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“…Similar to Definition 8 in [13] and Definition 2.9 in [14], we give the definition of Hyers-Ulam stability for C 1 solution of (2).…”

Section: Lemma 3 ([12]mentioning

confidence: 99%

Hyers-Ulam stability for C1 solution of series-like iterative equation with variable coefficients

Xia¹,

Wang²

2020

ScienceAsia

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Hyers-Ulam stability is a basic sense of stability for functional equations. In the present paper we discuss the Hyers-Ulam stability of series-like iterative equations with variable coefficients. By the construction of a uniformly convergent sequence of functions we prove that if we can find a C 1 approximate solution of such an equation, then there must be a unique C 1 solution of this equation which is close to the C 1 approximate solution.

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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: 99%

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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Hyers–Ulam stability of the iterative equation with a general boundary restriction

Cited by 4 publications

References 20 publications

On the Ulam Type Stability of Nonlinear Volterra Integral Equations

On the Ulam Type Stability of Nonlinear Volterra Integral Equations

Hyers-Ulam stability for C1 solution of series-like iterative equation with variable coefficients

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

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