On Ulam Stabilities of Delay Hammerstein Integral Equation

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Tunç O., Tunç C.

Symmetry, vol.15, no.9, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 9
  • Publication Date: 2023
  • Doi Number: 10.3390/sym15091736
  • Journal Name: Symmetry
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Banach FPT, Bielecki metric, Hammerstein IE, HU stability, HUR stability
  • Van Yüzüncü Yıl University Affiliated: Yes


In this paper, we consider a Hammerstein integral equation (Hammerstein IE) in two variables with two variables of time delays. The aim of this paper is to investigate the Hyers–Ulam (HU) stability and Hyers–Ulam–Rassias (HUR) stability of the considered IE via Banach’s fixed point theorem (Banach’s FPT) and the Bielecki metric. The proofs of the new outcomes of this paper are based on these two basic tools. As the new contributions of the present study, here, for the first time, we develop the outcomes that can be found in the earlier literature on the Hammerstein IE, including variable time delays. The present study also includes complementary outcomes for the symmetry of Hammerstein IEs. Finally, a concrete example is given at the end of this study for illustrations.