ULAM’S TYPE STABILITY OF IMPULSIVE DIFFERENTIAL EQUATIONS WITH SEVERAL TIME-VARYING DELAYS

Tunç C., Tunç O.

Fixed Point Theory, cilt.27, sa.1, ss.437-454, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 27 Sayı: 1
  • Basım Tarihi: 2026
  • Doi Numarası: 10.24193/fpt-ro.2026.1.26
  • Dergi Adı: Fixed Point Theory
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.437-454
  • Anahtar Kelimeler: Banach contraction mapping principle, Delay differential equation, Gronwall lemma and inequality, time-varying delays; Ulam’s type stability
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

We investigate two concepts of Ulam’s type stability for an impulsive delay differential equation (DDE) with several time-varying delays. By applying Banach contraction mapping principle (Banach CMP), the integral inequality of Gronwall type for piecewise continuous functions and abstract Gronwall lemma, Ulam-Hyers stability and Ulam– Hyers-Rassias stability results for impulsive DDE with several time-varying delays are obtained. We also provide an example to demonstrate how our findings might be applied. In addition, this article offers some novel complementary findings related to the qualitative theory of impulsive DDEs with multiple time-varying delays.