Dergiler / Hacettepe Journal of Mathematics and Statistics / 2013 / Cilt: 42 - Sayı: 5

APPROXIMATE QUADRATIC FUNCTIONAL EQUATION IN FELBIN’S TYPE NORMED LINEAR SPACES

Sayfa
501–516
Yayın Tarihi
2013-05-01
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)

Soc. 72 (1978), 297–300.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we prove the generalized Hyers–Ulam–Rassias stability ofquadratic functional equation in Felbin’s type normed linear spaces byusing the direct and fixed point methods.
📊
Temel Bulgular & Veri:The concept of Hyers-UlamRassias stability originated from Th.
💡
Sonuç & Katkı:Soc. 72 (1978), 297–300.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Analysis · fixed point · fuzzy numbers

Abstract

In this paper, we prove the generalized Hyers–Ulam–Rassias stability ofquadratic functional equation in Felbin’s type normed linear spaces byusing the direct and fixed point methods. The concept of Hyers-UlamRassias stability originated from Th. M. Rassias’ stability theorem thatappeared in his paper: On the stability of the linear mapping in Banachspaces, Proc. Amer. Math. Soc. 72 (1978), 297–300.

🔖

Bu Makaleye Atıf Yap

MORADLOU, F., REZAEE, S., SADEQİ, İ. (2013). APPROXIMATE QUADRATIC FUNCTIONAL EQUATION IN FELBIN’S TYPE NORMED LINEAR SPACES. Hacettepe Journal of Mathematics and Statistics, Cilt: 42 - Sayı: 5, 501–516. https://ajindex.com/articles/669593

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (17)

  1. Acz´ el, J., Dhombres, J. Functional Equations in Several Variables, Cambridge University Press, 1989.
  2. Aoki, T. On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2, 64–66, 1950.
  3. Bag, T. and Samanta, S. K. Fixed point theorems in Felbin type fuzzy normed linear spaces, J. Fuzzy Math. 16(1), 243–260, 2008.
  4. Bag, T., Samanta, S. K. A comparative study of fuzzy norms on a linear space, Fuzzy Sets Syst. 159(6), 670–684, 2008.
  5. Baker, J. A. The stability of certain functional equations, Proc. Amer. Math. Soc., 112, 729–732, 1991.
  6. Borelli, C., Forti, G.L. On a general Hyers–Ulam stability result, Internat. J. Math. Math. Sci. 18, 229–236, 1995.
  7. Bourgin, D.G. Classes of transformations and bordering transformations, Bull. Amer. Math. Soc. 57, 223–237, 1951. C˘ adariu, L., Radu, V. Fixed points and the stability of quadratic functional equations, An. Univ. Timi¸ soara, Ser. Mat.-Inform. 41, 25–48, 2003.
  8. Czerwik, S. The stability of the quadratic functional equation, in: Th. M. Rassias, J. Tabor (Eds.), Stability of Mappings of Hyers–Ulam Type, Hadronic Press, Florida, 81–91, 1994.
  9. Czerwik, S. Functional Equations and Inequalities in Several Variables, World Scientific Publ.Co., New Jersey, London, Singapore, 2002.
  10. Diaz, J., Margolis, B. A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74, 305–309, 1968.
  11. Eskandani, G.Z. On the Hyers-ˆ uUlam-ˆ uRassias stability of an additive functional equation in quasi-Banach spaces, J. Math. Anal. Appl. 345, 405–409, 2008.
  12. Faizev, V.A., Rassias, Th. M., Sahoo, P.K. The space of (Ψ, γ) - additive mappings on semigroups, Transactions of the Amer. Math. Soc. 354(11), 4455–4472, 2002.
  13. Felbin, C. Finite dimensional fuzzy normed linear spaces, Fuzzy Sets Syst. 48, 239–248, 199 Gantner, T., Steinlage, R., Warren, R. Compactness in fuzzy topological spaces, J. Math. Anal. Appl. 62, 547–562, 1978. Gˇ avruta, P. A generalization of the Hyers–Ulam–Rassias stability of approximately additive mappings J. Math. Anal. Appl. 184, 431–436, 1994.
  14. Hoehle, U. Fuzzy real numbers as Dedekind cuts with respect to a multiple-valued logic, Fuzzy Sets Syst. 24, 263–278, 1987.
  15. Hyers, D. H. On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27, 222–224, 1941.
  16. Hyers, D. H., Isac, G., Rassias, Th. M. Stability of Functional Equations in Several Variables, Birkh¨ auser, Basel, 1998.
  17. Jun, K., Lee, Y. On the Hyers–Ulam–Rassias st