New Results on Ulam Stabilities of Nonlinear Integral Equations


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Tunç O., Tunç C., Yao J.

Mathematics, vol.12, no.5, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 5
  • Publication Date: 2024
  • Doi Number: 10.3390/math12050682
  • Journal Name: Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Gronwall lemma, higher dimensions, HU stability, HUR stability, Volterra integral equation
  • Van Yüzüncü Yıl University Affiliated: Yes

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.