Journals / Gazi University Journal of Science / 2019 / Cilt: 32 - Sayı: 4

Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations

Pages
1238–1252
Publication Date
2022-10-19
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

This paper examines Hyers-Ulam (HU), Hyers-Ulam-Rassias (HUR) and HyersUlam-Rassias-Gavruta (HURG) stability of the first-order differential equation including Bernoulli’s, Riccati and Abel with given initial condition.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper examines Hyers-Ulam (HU), Hyers-Ulam-Rassias (HUR) and HyersUlam-Rassias-Gavruta (HURG) stability of the first-order differential equation including Bernoulli’s, Riccati and Abel with given initial condition.
📊
Key Findings & Data:This paper examines Hyers-Ulam (HU), Hyers-Ulam-Rassias (HUR) and HyersUlam-Rassias-Gavruta (HURG) stability of the first-order differential equation including Bernoulli’s, Riccati and Abel with given initial condition.
💡
Conclusion & Impact:This paper examines Hyers-Ulam (HU), Hyers-Ulam-Rassias (HUR) and HyersUlam-Rassias-Gavruta (HURG) stability of the first-order differential equation including Bernoulli’s, Riccati and Abel with given initial condition.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

This paper examines Hyers-Ulam (HU), Hyers-Ulam-Rassias (HUR) and HyersUlam-Rassias-Gavruta (HURG) stability of the first-order differential equation including Bernoulli’s, Riccati and Abel with given initial condition.

🔖

Cite This Article

MISIR, A., ÖĞREKÇİ, S., BAŞCI, Y. (2022). Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations. Gazi University Journal of Science, Cilt: 32 - Sayı: 4, 1238–1252. https://ajindex.com/articles/521322

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  1. Hyers, D.H.,“On the stability of the linear functional equation”, Proceeding of the National Academy of Sciences of the United States of America, 27: 222-224, (1941)
  2. Bourgin, D.G., “Classes of transformations and bordering transformations”, Bulletin of the American Mathematical Society, 57: 223-237, (1951)
  3. Aoki, T., “On the stability of the linear transformation in Banach spaces”, Journal of Mathematical Society of the Japan, 2: 64-66, (1950)
  4. Rassias, Th.M. “On the stability of the linear mapping in Banach spaces”, Proceeding American Mathematical Society, 72(2): 297-300, (1978)
  5. Obloza, M., “Hyers stability of the linear differential equation”, Rocznik Nauk-Dydakt Prace Matematik, 13(1): 259-270, (1993)
  6. Obloza, M., “Connections between Hyers and Lyapunov stability of the ordinary differential equations”, Rocznik Nauk-Dydakt Prace Matematik, 14(1): 141-146, (1997)
  7. Alsina, C., Ger, R., “On some inequalities and stability results related to the exponential function”, Journal of Mathematical Inequalities, 2(4): 373-380, (1998)
  8. Miura, T., “On the Hyers-Ulam stability of a differentiable map”, Scientiae Mathematicae Japonicae, 55: 17-24, (2002)
  9. Miura, T., Takahasi, S.E., Choda, H., “On the Hyers-Ulam stability of real continuous function valued differentiable map”, Tokyo Journal of Mathematics, 24: 467-476, (2001)
  10. Takahasi, S.E., Miura, T., Miyajima, S., “On the Hyers-Ulam stability of the Banach space-valued differential equation 𝑦′ = 𝜆𝑦”, Bulletin of Korean Mathematical Society, 39: 309-315, (2002)
  11. Miura, T., Jung, S.M., Takahasi, S.E., “Hyers-Ulam-Rassias stability of the Banach space valued linear differential equations 𝑦′ = 𝜆𝑦”, Journal of the Korean Mathematical Society, 41: 995-1005, (2004)
  12. Jung, S.M., “Hyers-Ulam stability of linear differential equations of first order”, Applied Mathematics Letters, 17(10): 1135-1140, (2004)
  13. Jung, S.M., “Hyers-Ulam stability of linear differential equations of first order II”, Applied Mathematics Letters, 19(9): 854-858, (2006)
  14. Miura, T., Miyajima, S., Takahasi, S.E., “A characterization of Hyers-Ulam stability of first order linear differential operators”, Journal of Mathematical Analysis Applications, 286: 136-146, (2003)
  15. Takahasi, S.E., Takagi, H., Miura, T., Miyajima, S.,“The Hyers-Ulam stability constants of first order linear differential operators”, Journal of Mathematical Analysis Applications, 296: 403-409, (2004)
  16. Jung, S.M.,