Journals / Sigma Mühendislik ve Fen Bilimleri Dergisi / 2020 / Cilt: 38 - Sayı: 3

ON STABILITY OF SOME INTEGRAL EQUATIONS IN 2-BANACH SPACES

Pages
1261–1268
Publication Date
2021-10-05
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)

In this way, we obtain results in 2-Banach Spaces.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The objective of this article is to investigate the Ulam-Hyres stability and Ulam-Hyres-Rassias stability for some general integral equations f(x)=∫_E F(x,f(x))dx, x∈E, where E is a nonempty set of a Banach space.
📊
Key Findings & Data:The main tool used in the analysis is a recent fixed point theory.
💡
Conclusion & Impact:In this way, we obtain results in 2-Banach Spaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Ulam stability · integral equation · fixed point theory

Abstract

The objective of this article is to investigate the Ulam-Hyres stability and Ulam-Hyres-Rassias stability for some general integral equations f(x)=∫_E F(x,f(x))dx, x∈E, where E is a nonempty set of a Banach space. The main tool used in the analysis is a recent fixed point theory. In this way, we obtain results in 2-Banach Spaces.

🔖

Cite This Article

EL-HADY, E., ÖĞREKÇİ, S. (2021). ON STABILITY OF SOME INTEGRAL EQUATIONS IN 2-BANACH SPACES. Sigma Mühendislik ve Fen Bilimleri Dergisi, Cilt: 38 - Sayı: 3, 1261–1268. https://ajindex.com/articles/419070

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (18)

  1. Ulam, S. M. (1960) Problems in Modern Mathematics, Chapter VI, Science Editions, Wiley, New York
  2. Ulam, S. M. (1960) A Collection of the Mathematical Problems, Interscience Publ., New York
  3. Hyers, D. H., Isac, G., Rassias, TH. M. (1998) Stability of Functional Equation in Several Variables, Rirkh¨auser, Basel
  4. Rassias, TH. M. (2000) On the stability of functional equations and a problem of Ulam, Acta Applicandae Mathematicae, 62, 23–130
  5. Rassias, TH. M. (2000) On the stability of functional equations in Banach spaces, J. Math. Anal. Appl., 251, 264–284
  6. Rassias, TH. M. (2000) The problem of S. M. Ulam for approximately multiplicative mappings, J. Math. Anal. Appl., 246, 352–378
  7. Rassias, TH. M. (2003) Functional Equations, Inequalities and Applications, Kluwer Academic, Dordrecht, Boston and London
  8. Brillouët-Belluot, N., and Brzdek, J. and Ciepliński, K. (2012) On some recent developments in Ulam’s type stability, Abstract and Applied Analysis, vol. 2012, Article ID 716936, 41 pages
  9. G. L. Forti (1995) Hyers-Ulam stability of functional equations in several variables, Aequationes Mathematicae, 50(1-2), 143–190
  10. Hyers, D. H. (1941) On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27, 222–224
  11. Aoki, T. (1950) On the stability of the linear transformation in Banach spaces, Journal of the Mathematical Society of Japan, 2(1-2), 64–66 [12] Bourgin, D. G. (1949) Approximately isometric and multiplicative transformations on continuous function rings, Duke Math. J. 16, 385–397
  12. Rassias, TH. M. (1978) On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, 297–300
  13. Alsina, C. and Ger, R. (1998) On some inequalities and stability results related to the exponential function, J. Inequal. Appl., 2(4), 373–380
  14. Jung, S.-M. (2004) Hyers-Ulam stability of linear differential equations of first order, Appl. Math. Lett., 17(10), 1135–1140
  15. Jung, S.-M. (2006) Hyers-Ulam stability of a system of first order linear differential equations with constant coefficients, J. Math. Anal. Appl. 320(2), 549–561
  16. Jung, S.-M. (2006) Hyers-Ulam stability of linear differential equations offirst order. II, Appl. Math. Lett., 19(9), 854–858
  17. Jung, S.-M. (2010) A fixed point approach to the stability of differential equations y'=F(x,y), Bull. Malays. Math. Sci. Soc., 33(1), 47–56
  18. Miura, T., Miyajima, S. and Takahasi, S.-E. (2003) A characterization of H