New Results on Ulam Stabilities of Nonlinear Integral Equations

Osman Tunç, Cemil Tunç () and Jen-Chih Yao
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Osman Tunç: Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Van 65080, Turkey
Cemil Tunç: Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van 65080, Turkey
Jen-Chih Yao: Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 404, Taiwan

Mathematics, 2024, vol. 12, issue 5, 1-13

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.

Keywords: Volterra integral equation; HUR stability; HU stability; Gronwall lemma; higher dimensions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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