10.1186/2251-7456-6-55

RETRACTED ARTICLE: Approximation of Jordan homomorphisms in Jordan-Banach algebras

HTML PDF
  • Madjid Eshaghi Gordji*1,
  • Najmeh Karimipour Samani1,
  • Choonkil Park2,
  1. Department of Mathematics, Semnan University, Semnan, 35195-363, IR
  2. Research Institute for Natural Sciences, Hanyang University, Seoul, 133-791, KR

Published in Issue 2012-10-24

How to Cite

Gordji, M. E., Samani, N. K., & Park, C. (2012). RETRACTED ARTICLE: Approximation of Jordan homomorphisms in Jordan-Banach algebras. Mathematical Sciences, 6(1). https://doi.org/10.1186/2251-7456-6-55
Crossref
Scopus
Google Scholar
Europe PMC

HTML views: 10

PDF views: 72

Abstract

Abstract Using the direct method based on the Hyers-Ulam-Rassias stability, we investigate and prove the Hyers-Ulam stability of Jordan homomorphisms in Jordan-Banach algebras for the functional equation ∑k=2n∑i1=2k∑i2=i1+1k+1⋯∑in-k+1=in-k+1nf∑i=1,i≠i1,⋯,in-k+1nxi-∑r=1n-k+1xir+f∑i=1nxi-2n-1f(x1)=0, where n is an integer greater than 1. We have proved the Hyers-Ulam stability of Jordan homomorphisms in Jordan-Banach algebras for the above functional equation.

Keywords

  • Hyers-Ulam stability,
  • Jordan homomorphism,
  • Jordan algebra,
  • 39B52,
  • 17C65
HTML PDF

References

  1. Ulam (1960) Interscience Publishers
  2. Hyers (1941) On the stability of the linear functional equation (pp. 222-224) https://doi.org/10.1073/pnas.27.4.222
  3. Aoki (1950) On the stability of the linear transformation in Banach spaces (pp. 64-66) https://doi.org/10.2969/jmsj/00210064
  4. Rassias (1978) On the stability of the linear mapping in Banach spaces Proc (pp. 297-300) https://doi.org/10.1090/S0002-9939-1978-0507327-1
  5. Găvruta (1994) A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings (pp. 431-436) https://doi.org/10.1006/jmaa.1994.1211
  6. Badora (2002) On approximate ring homomorphisms (pp. 589-597) https://doi.org/10.1016/S0022-247X(02)00293-7
  7. Badora (2006) On approximate derivations (pp. 167-173)
  8. Czerwik (2003) Hadronic Press
  9. Gajda (1991) On stability of additive mappings (pp. 431-434) https://doi.org/10.1155/S016117129100056X
  10. Gavruta and Gavruta (2010) A new method for the generalized Hyers-Ulam-Rassias stability 1(2) (pp. 11-18)
  11. Jun and Lee (1999) A generalization of the Hyers-Ulam-Rassias stability of Jensen’s equation (pp. 305-315) https://doi.org/10.1006/jmaa.1999.6546
  12. Khodaei and Kamyar (2010) Fuzzy approximately additive mappings 1(2) (pp. 44-53)
  13. Khodaei and Rassias (2010) Approximately generalized additive functions in several variables 1(1) (pp. 22-41)
  14. Park (2002) On the stability of the linear mapping in Banach modules (pp. 711-720) https://doi.org/10.1016/S0022-247X(02)00386-4
  15. Park (2003) Modified Trif’s functional equations in Banach modules over a C∗-algebra and approximate algebra homomorphisms (pp. 93-108) https://doi.org/10.1016/S0022-247X(02)00573-5
  16. Park (2004) Lie ∗-homomorphisms between Lie C∗-algebras and Lie ∗-derivations on Lie C∗-algebras (pp. 419-434) https://doi.org/10.1016/j.jmaa.2003.10.051
  17. Park and Park (2002) On the Jensen’s equation in Banach modules (pp. 523-531)
  18. Park and Eshaghi Gordji (2010) Comment on “Approximate ternary Jordan derivations on Banach ternary algebras” [Bavand Savadkouhi et al. J. Math. Phys. 50, 042303 (2009)] https://doi.org/10.1063/1.3299295
  19. Park and Najati (2010) Generalized additive functional inequalities in Banach algebras 1(2) (pp. 54-62)
  20. Park and Rassias (2010) Isomorphisms in unital C∗-algebras 1(2) (pp. 1-10)
  21. Rassias (1982) On approximation of approximately linear mappings by linear mappings (pp. 126-130) https://doi.org/10.1016/0022-1236(82)90048-9
  22. Rassias (1984) On approximation of approximately linear mappings by linear mappings (pp. 445-446)
  23. Rassias (1985) On a new approximation of approximately linear mappings by linear mappings (pp. 193-196)
  24. Rassias (1989) Solution of a problem of Ulam (pp. 268-273) https://doi.org/10.1016/0021-9045(89)90041-5
  25. Rassias (1990) Problem 16; 2, Report of the 27th international symposium on functional equations (pp. 292-293)
  26. Rassias (2003) Kluwer https://doi.org/10.1007/978-94-017-0225-6
  27. Shakeri et al. (2010) Stability of the quadratic functional equation in non-Archimedean L-fuzzy normed spaces 1(2) (pp. 72-83)
  28. Kadison and Pedersen (1985) Means and convex combinations of unitary operators (pp. 249-266)