KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2011 / Cilt: 40 - Sayı: 5

FUZZY STABILITY OF A FUNCTIONAL EQUATION RELATED TO INNER PRODUCT SPACES

Sun Young JANG
Choonkil PARK
Sayfa
711–723
Yayın Tarihi
2022-10-18
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 paper, we prove the generalized Hyers-Ulam stability of the functional equation (0.1) in fuzzy Banach spaces.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:The fuzzy stability problems for the Cauchy quadratic functional equation and the Jensen quadratic functional equation in fuzzy Banach spaces have been investigated by Moslehian et al.
📊
Temel Bulgular & Veri:Rassias introduced the following equality Xm i,j=1 kxi − xjk 2 = 2m Xm i=1 kxik 2 , Xm i=1 xi = 0, for a fixed integer m ≥ 3.
💡
Sonuç & Katkı:In this paper, we prove the generalized Hyers-Ulam stability of the functional equation (0.1) in fuzzy Banach spaces.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Fuzzy Banach space · Functional equation related to inner product space · Generalized Hyers-Ulam stability

Abstract

The fuzzy stability problems for the Cauchy quadratic functional equation and the Jensen quadratic functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. Th. M. Rassias introduced the following equality Xm i,j=1 kxi − xjk 2 = 2m Xm i=1 kxik 2 , Xm i=1 xi = 0, for a fixed integer m ≥ 3. By the above equality, we define the following functional equation(0.1) Xm i,j=1 f(xi − xj ) = 2m Xmi=1 f(xi), Xm i=1 xi = 0. In this paper, we prove the generalized Hyers-Ulam stability of the functional equation (0.1) in fuzzy Banach spaces.

🔖

Bu Makaleye Atıf Yap

JANG, S. Y., PARK, C. (2022). FUZZY STABILITY OF A FUNCTIONAL EQUATION RELATED TO INNER PRODUCT SPACES. Hacettepe Journal of Mathematics and Statistics, Cilt: 40 - Sayı: 5, 711–723. https://ajindex.com/articles/530554

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (20)

  1. Aoki, T. On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2, 64–66, 1950.
  2. Bag, T. and Samanta, S. K. Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math. 11, 687–705, 2003.
  3. Bag, T. and Samanta, S. K. Fuzzy bounded linear operators, Fuzzy Sets and Systems 151, 513–547, 2005.
  4. Baktash, E., Cho, Y. J., Jalili, M., Saadati, R. and Vaezpour, S. M. On the stability of cubic mappings and quadratic mappings in random normed spaces, J. Inequal. Appl. 2008, Art. ID 902187, 2008.
  5. Cheng, S. C. and Mordeson, J. M. Fuzzy linear operators and fuzzy normed linear spaces, Bull. Calcutta Math. Soc. 86, 429–436, 1994.
  6. Cholewa, P. W. Remarks on the stability of functional equations, Aequationes Math. 27, 76–86, 1984.
  7. Czerwik, P. Functional Equations and Inequalities in Several Variables (World Scientific Publishing Company, New Jersey, Hong Kong, Singapore and London, 2002).
  8. Czerwik, S. On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg 62, 59–64, 1992.
  9. Czerwik, S. The stability of the quadratic functional equation, in: (Stability of mappings of Hyers-Ulam type, Hadronic Press,
  10. Palm Harbor, FL, 1994), 81–91.
  11. Felbin, C. Finite dimensional fuzzy normed linear spaces, Fuzzy Sets and Systems 48, 239– 248, 1992.
  12. Gajda, Z. On stability of additive mappings, Internat. J. Math. Math. Sci. 14, 431–434, 1991. G˘avruta, P. A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184, 431–436, 1994.
  13. Hyers, D. H. On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27, 222–224, 1941.
  14. Hyers, D. H., Isac, G. and Rassias, Th. M. Stability of Functional Equations in Several Variables(Birkh¨auser, Basel, 1998).
  15. Jung, S. Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis (Hadronic Press lnc., Palm Harbor, Florida, 2001).
  16. Katsaras, A. K. Fuzzy topological vector spaces II, Fuzzy Sets and Systems 12, 143–154, 1984.
  17. Kramosil, I. and Michalek, J. Fuzzy metric and statistical metric spaces, Kybernetica 11, 326–334, 1975.
  18. Krishna, S. V. and Sarma, K. K. M. Separation of fuzzy normed linear spaces, Fuzzy Sets and Systems 63, 207–217, 1994.
  19. Mirmostafaee, A. K., Mirzavaziri, M. and Moslehian, M. S. Fuzzy stability of the Jensen functional equation, Fuzzy Sets and Systems 159, 730–738, 2008.
  20. Mirmostafaee, A. K. and Moslehian, M. S. Fuzzy versions of Hyers-Ulam-Rassias theorem, Fuzzy Sets and Systems 159, 720–729, 2008