KaydedilenlerDerginizi ekleyin

Dergiler / Sigma Mühendislik ve Fen Bilimleri Dergisi / 2026 / Volume: 38 Issue: 3

ON STABILITY OF SOME INTEGRAL EQUATIONS IN 2-BANACH SPACES

El-sayed El-hady(Mathematics Department, College of Science, Jouf University)0000-0002-4955-0842
Süleyman Öğrekçi(Department of Mathematics, Amasya University)0000-0003-1205-6848
Sayfa
—
Yayın Tarihi
2021-10-05
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez: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.
📊
Temel Bulgular & Veri:The main tool used in the analysis is a recent fixed point theory.
💡
Sonuç & Katkı:In this way, we obtain results in 2-Banach Spaces.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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.

🔖

Bu Makaleye Atıf Yap

El-hady, E., Öğrekçi, S. (2021). ON STABILITY OF SOME INTEGRAL EQUATIONS IN 2-BANACH SPACES. Sigma Mühendislik ve Fen Bilimleri Dergisi, Volume: 38 Issue: 3. https://ajindex.com/articles/1344801

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (35)

  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.
  2. Hyers, D. H., Isac, G., Rassias, TH. M. (1998) Stability of Functional Equation in Several Variables, Rirkh¨auser, Basel.
  3. Rassias, TH. M. (2000) On the stability of functional equations and a problem of Ulam, Acta Applicandae Mathematicae, 62, 23–130.
  4. Rassias, TH. M. (2000) On the stability of functional equations in Banach spaces, J. Math. Anal. Appl., 251, 264–284.
  5. Rassias, TH. M. (2000) The problem of S. M. Ulam for approximately multiplicative mappings, J. Math. Anal. Appl., 246, 352–378.
  6. Rassias, TH. M. (2003) Functional Equations, Inequalities and Applications, Kluwer Academic, Dordrecht, Boston and London.
  7. 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.
  8. G. L. Forti (1995) Hyers-Ulam stability of functional equations in several variables, Aequationes Mathematicae, 50(1-2), 143–190.
  9. Hyers, D. H. (1941) On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27, 222–224.
  10. 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
  11. 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 Hyers-Ulam stability of first order linear differential operators, J. Math. Anal. Appl., 286(1), 136–146.
  19. Obloza, M. (1993) Hyers stability of the linear differential equation, Rocznik Nauk.-Dydakt. Prace Mat., 13, 259–270.
  20. Obloza, M. (1997) Connections between Hyers and Lyapunov stability of the ordinary differential equations, Rocznik Nauk.-Dydakt.
  21. Prace Mat., 14, 141–146. [22] Akkouchi, M. and Elqorachi, E. (2004) On Hyers-Ulam stability of cauchy and Wilson equations, Georgiam Math. J., 11 (1), 69–82.
  22. Akkouchi, M. and Elqorachi, E. (2005) On Hyers-Ulam stability of the generalized Cauchy and Wilson equations, Publicationes Mathematicae, 66(3–4), 3. [24] Baker, J. A. (1991) The stability of certain functional equations, Proceedings of the American Mathematical Society, 112(3), 729–732.
  23. Akkouchi, M. (2011) Hyers-Ulam-Rassias stability of nonlinear volterra integral equations via a fixed point approach, Acta Universitatis Apulensis, 26, (257–266).
  24. Diaz, J. B. and Margolis, B. (1968) A fixed point theorem of the alternative, for contractions on a generalized complete metric space, Bulletin ofthe American Mathematical Society, 74, 305–309.
  25. Ciepliński, K. (2012) Applications of fixed point theorems to the Hyers-Ulam stability of functional equations-a survey, Annals ofFunctional Analysis, 3(1), 151–164.
  26. BrzdĘk, J., Chudziak, J. and Páles, Z. (2011) A fixed point approach to stability of functional equations, Nonlinear Analysis. Theory, Methods and Applications A, 74(17), 6728–6732.
  27. BrzdĘk, J. and Ciepliński, K., (2011) A fixed point approach to the stability of functional equations in non-archimedean metric spaces, Nonlinear Analysis. Theory, Methods and Applications A, 74(18), 6861–6867.
  28. Freese, R. W., Cho, Y. J. (2001) Geometry of Linear 2-normed Spaces. Hauppauge, NY: Nova Science Publishers, Inc.
  29. Park, W. G., (2011) Approximate additive mappings in 2-Banach spaces and related topics, J. Math. Anal., 376(1), 193–202.
  30. BrzdĘk, J. and Ciepliński, K., (2018) On a fixed point theorem in 2-Banach spaces and some of its applications, Acta Mathematica Scientia, 38(2), 377–390.
  31. Radu, V. (2003) The fixed point alternative and the stability of functional equations, Fixed Point Theory, 4(1), 91–96.
  32. Ca ̆dariu, L. and Radu, V. (2003) Fixed points and the stability of Jensen’s functional equation, J. Inequal. Pure Appl. Math., 4(1), Art. ID 4.
  33. Gajda, Z. (1991) On stability of additive mappings, Internat. J. Math. Math. Sci., 14, 431–434.
  34. Jung, S.-M. (1998) Hyers-Ulam-Rassias stability of Jensen’s equation and its application, Proc. Amer. Math. Soc., 126, 3137–3143.
  35. Jian, W. (2001) Some further generalizations of the Hyers-Ulam-Rassias stability of functional equations, J. Math. Anal. Appl., 263, 406–423.