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New Results on Ulam Stabilities of Nonlinear Integral Equations

Author

Listed:
  • Osman Tunç

    (Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Van 65080, Turkey
    These authors contributed equally to this work.)

  • Cemil Tunç

    (Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van 65080, Turkey
    These authors contributed equally to this work.)

  • Jen-Chih Yao

    (Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 404, Taiwan
    Academy of Romanian Scientists, 50044 Bucharest, Romania
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Osman Tunç & Cemil Tunç & Jen-Chih Yao, 2024. "New Results on Ulam Stabilities of Nonlinear Integral Equations," Mathematics, MDPI, vol. 12(5), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:682-:d:1346401
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