Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2011, Article ID 513128, 12 pages
http://dx.doi.org/10.1155/2011/513128
Research Article

Nearly Jordan βˆ— -Homomorphisms between Unital 𝐢 βˆ— -Algebras

1Department of Mathematics, Urmia University, Urmia, Iran
2Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
3Center of Excellence in Nonlinear Analysis and Applications (CENAA), Semnan University, Semnan, Iran

Received 26 February 2011; Revised 7 April 2011; Accepted 10 April 2011

Academic Editor: Irena Lasiecka

Copyright © 2011 A. Ebadian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. M. Ulam, Problems in Modern Mathematics, chapter 6, Wiley, New York, NY, USA, 1940.
  2. D. H. Hyers, β€œOn the stability of the linear functional equation,” Proceedings of the National Academy of Sciences of the United States of America, vol. 27, pp. 222–224, 1941. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  3. T. Aoki, β€œOn the stability of the linear transformation in Banach spaces,” Journal of the Mathematical Society of Japan, vol. 2, pp. 64–66, 1950. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  4. T. M. Rassias, β€œOn the stability of the linear mapping in Banach spaces,” Proceedings of the American Mathematical Society, vol. 72, pp. 297–300, 1978. View at Google Scholar
  5. J. M. Rassias, β€œOn approximation of approximately linear mappings by linear mappings,” Journal of Functional Analysis, vol. 46, no. 1, pp. 126–130, 1982. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  6. J. M. Rassias and M. J. Rassias, β€œAsymptotic behavior of alternative Jensen and Jensen type functional equations,” Bulletin des Sciences Mathematiques, vol. 129, no. 7, pp. 545–558, 2005. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  7. J. M. Rassias and M. J. Rassias, β€œOn the Ulam stability of Jensen and Jensen type mappings on restricted domains,” Journal of Mathematical Analysis and Applications, vol. 281, no. 2, pp. 516–524, 2003. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  8. S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific, River Edge, NJ, USA, 2002. View at Publisher Β· View at Google Scholar
  9. D. H. Hyers, G. Isac, and T. M. Rassias, Stability of Functional Equations in Several Variables, Birkhäuser, Basel, Switzerland, 1998.
  10. S. M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, Fla, USA, 2001.
  11. R. Badora, β€œOn approximate ring homomorphisms,” Journal of Mathematical Analysis and Applications, vol. 276, no. 2, pp. 589–597, 2002. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  12. J. Baker, J. Lawrence, and F. Zorzitto, β€œThe stability of the equation f(x+y)=f(x)f(y),” Proceedings of the American Mathematical Society, vol. 74, no. 2, pp. 242–246, 1979. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  13. D. G. Bourgin, β€œApproximately isometric and multiplicative transformations on continuous function rings,” Duke Mathematical Journal, vol. 16, pp. 385–397, 1949. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  14. D. H. Hyers and T. M. Rassias, β€œApproximate homomorphisms,” Aequationes Mathematicae, vol. 44, no. 2-3, pp. 125–153, 1992. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  15. T. Miura, S. E. Takahasi, and G. Hirasawa, β€œHyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras,” Journal of Inequalities and Applications, no. 4, pp. 435–441, 2005. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  16. C. Park, β€œHyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras,” Bulletin des Sciences Mathématiques, vol. 132, no. 2, pp. 87–96, 2008. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  17. C. Park, β€œHomomorphisms between Poisson JC-algebras,” Bulletin of the Brazilian Mathematical Society. New Series. Boletim da Sociedade Brasileira de Matemática, vol. 36, no. 1, pp. 79–97, 2005. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  18. C. Park and J. M. Rassias, β€œStability of the Jensen-type functional equation in C-algebras: a fixed point approach,” Abstract and Applied Analysis, Article ID 360432, 17 pages, 2009. View at Google Scholar
  19. T. M. Rassias, β€œOn the stability of functional equations and a problem of Ulam,” Acta Applicandae Mathematicae, vol. 62, no. 1, pp. 23–130, 2000. View at Google Scholar
  20. K. W. Jun and Y. H. Lee, β€œA generalization of the Hyers-Ulam-Rassias stability of Jensen's equation,” Journal of Mathematical Analysis and Applications, vol. 238, no. 1, pp. 305–315, 1999. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  21. C. Park and W. Park, β€œOn the Jensen's equation in Banach modules,” Taiwanese Journal of Mathematics, vol. 6, no. 4, pp. 523–531, 2002. View at Google Scholar Β· View at Zentralblatt MATH
  22. B. E. Johnson, β€œApproximately multiplicative maps between Banach algebras,” Journal of the London Mathematical Society, vol. 37, no. 2, pp. 294–316, 1988. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  23. L. G. Brown and G. K. Pedersen, β€œC-algebras of real rank zero,” Journal of Functional Analysis, vol. 99, no. 1, pp. 131–149, 1991. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  24. C. Park, D. H. Boo, and J. S. An, β€œHomomorphisms between C-algebras and linear derivations on C-algebras,” Journal of Mathematical Analysis and Applications, vol. 337, no. 2, pp. 1415–1424, 2008. View at Publisher Β· View at Google Scholar
  25. R. V. Kadison and J. R. Ringrose, Fundamentals of the Theory of Operator Algebras: Elementary Theory, vol. 100 of Pure and Applied Mathematics, Academic Press, New York, NY,USA, 1983.
  26. L. Cădariu and V. Radu, β€œThe fixed points method for the stability of some functional equations,” Carpathian Journal of Mathematics, vol. 23, no. 1-2, pp. 63–72, 2007. View at Google Scholar Β· View at Zentralblatt MATH
  27. L. Cădariu and V. Radu, β€œFixed points and the stability of quadratic functional equations,” Analele Universitatii de Vest din Timisoara, vol. 41, no. 1, pp. 25–48, 2003. View at Google Scholar
  28. L. Cădariu and V. Radu, β€œFixed points and the stability of Jensen's functional equation,” Journal of Inequalities in Pure and Applied Mathematics, vol. 4, no. 1, article 4, 2003. View at Google Scholar Β· View at Zentralblatt MATH
  29. M. Eshaghi Gordji, β€œJordan −homomorphisms between unital C−algebras: a fixed point approach,” Fixed Point Theory. In press.
  30. P. Gãvruta and L. Gãvruta, β€œA new method for the generalized Hyers-Ulam-Rassias stability,” International Journal of Nonlinear Analysis and Applications, vol. 1, no. 2, pp. 11–18, 2010. View at Google Scholar
  31. A. Ebadian, N. Ghobadipour, and M. Eshaghi Gordji, β€œA fixed point method for perturbation of bimultipliers and Jordan bimultipliers in C-ternary algebras,” Journal of Mathematical Physics, vol. 51, no. 10, 2010. View at Publisher Β· View at Google Scholar
  32. M. Eshaghi Gordji, β€œNearly ring homomorphisms and nearly ring derivations on non-Archimedean Banach algebras,” Abstract and Applied Analysis, Article ID 393247, 12 pages, 2010. View at Google Scholar
  33. M. Eshaghi Gordji and Z. Alizadeh, β€œStability and superstability of ring homomorphisms on non-archimedean banach algebras,” Abstract and Applied Analysis, vol. 2011, Article ID 123656, 10 pages, 2011. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  34. M. Eshaghi Gordji, M. Bavand Savadkouhi, M. Bidkham, C. Park, and J. R. Lee, β€œNearly Partial Derivations on Banach Ternary Algebras,” Journal of Mathematics and Statistics, vol. 6, no. 4, pp. 454–461, 2010. View at Google Scholar
  35. M. Eshaghi Gordji, A. Bodaghi, and I. A. Alias, β€œOn the stability of quadratic double centralizers and quadratic multipliers: a fixed point approach,” Journal of Inequalities and Applications, vol. 2011, Article ID 957541, 12 pages, 2011. View at Google Scholar
  36. M. Eshaghi Gordji, M. B. Ghaemi, S. Kaboli Gharetapeh, S. Shams, and A. Ebadian, β€œOn the stability of J-derivations,” Journal of Geometry and Physics, vol. 60, no. 3, pp. 454–459, 2010. View at Publisher Β· View at Google Scholar
  37. M. Eshaghi Gordji and H. Khodaei, Stability of Functional Equations, LAP- Lambert Academic Publishing, Saarbrücken, Germany, 2010.
  38. M. Eshaghi Gordji and H. Khodaei, β€œThe fixed point method for fuzzy approximation of a functional equation associated with inner product spaces,” Discrete Dynamics in Nature and Society, Article ID 140767, 15 pages, 2010. View at Google Scholar
  39. M. Eshaghi Gordji, H. Khodaei, and R. Khodabakhsh, β€œGeneral quartic-cubic-quadratic functional equation in non-Archimedean normed spaces,” University “Politehnica” of Bucharest, Scientific Bulletin Series A, vol. 72, no. 3, pp. 69–84, 2010. View at Google Scholar
  40. M. Eshaghi Gordji and A. Najati, β€œApproximately J-homomorphisms: a fixed point approach,” Journal of Geometry and Physics, vol. 60, no. 5, pp. 809–814, 2010. View at Publisher Β· View at Google Scholar
  41. R. Farokhzad and S. A. R. Hosseinioun, β€œPerturbations of Jordan higher derivations in Banach ternary algebras: an alternative fixed point approach,” International Journal of Nonlinear Analysis and Applications, vol. 1, no. 1, pp. 42–53, 2010. View at Google Scholar
  42. V. Radu, β€œThe fixed point alternative and the stability of functional equations,” Fixed Point Theory, vol. 4, no. 1, pp. 91–96, 2003. View at Google Scholar Β· View at Zentralblatt MATH
  43. I. A. Rus, Principles and Applications of Fixed Point Theory, Editura Dacia, Cluj-Napoca, Romania, 1979.
  44. L. Cădariu and V. Radu, β€œOn the stability of the Cauchy functional equation: a fixed point approach,” Grazer Mathematische Berichte, vol. 346, pp. 43–52, 2004. View at Google Scholar
  45. B. Margolis and J. B. Diaz, β€œA fixed point theorem of the alternative, for contractions on a generalized complete metric space,” Bulletin of the American Mathematical Society, vol. 126, pp. 305–309, 1968. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet