New Results on Ulam Stabilities of Nonlinear Integral Equations-Reference-Cited by-同舟云学术

New Results on Ulam Stabilities of Nonlinear Integral Equations

Published:2024-02-26 Issue:5 Volume:12 Page:682
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Tunç Osman¹^ORCID,Tunç Cemil²^ORCID,Yao Jen-Chih³⁴

Affiliation:

1. Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Van 65080, Turkey

2. Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van 65080, Turkey

3. Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 404, Taiwan

4. Academy of Romanian Scientists, 50044 Bucharest, Romania

Abstract

This article deals with the study of Hyers–Ulam stability (HU stability) and Hyers–Ulam–Rassias stability (HUR stability) for two classes of nonlinear Volterra integral equations (VIEqs), which are Hammerstein-type integral and Hammerstein-type functional integral equations, respectively. In this article, both the HU stability and HUR stability are obtained for the first integral equation and the HUR stability is obtained for the second integral equation. Among the used techniques, we present fixed point arguments and the Gronwall lemma as a basic tool. Two supporting examples are also provided to demonstrate the applications and effectiveness of the results.

Funder

MOST

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/5/682/pdf

Reference33 articles.

1. Burton, T.A. (2005). Volterra Integral and Differential Equations, Elsevier B.V.. [2nd ed.]. Mathematics in Science and Engineering 202.

2. Corduneanu, C. (1991). Integral Equations and Applications, Cambridge University Press.

3. Wazwaz, A.-M. (2011). Methods and Applications, Springer.

4. Existence and Ulam stability results for quadratic integral equations;Abbas;Lib. Math.,2015

5. On existence and asymptotic stability of solutions of a nonlinear integral equation;Rzepka;J. Math. Anal. Appl.,2003

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Existence and Stability of Solutions for p-Proportional ω-Weighted κ-Hilfer Fractional Differential Inclusions in the Presence of Non-Instantaneous Impulses in Banach Spaces;Fractal and Fractional;2024-08-14

2. Hyers–Ulam–Rassias stability of fractional delay differential equations with Caputo derivative;Mathematical Methods in the Applied Sciences;2024-05-18

3. New Results on the Ulam–Hyers–Mittag–Leffler Stability of Caputo Fractional-Order Delay Differential Equations;Mathematics;2024-04-28

4. On Ulam stabilities of iterative Fredholm and Volterra integral equations with multiple time-varying delays;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2024-04-02

5. A Qualitative Study of Solutions of Nonlinear Volterra Integral Equation in the Plane, from the Perspective of Shiba Bounded Variation;International Journal of Mathematics and Mathematical Sciences;2024-01