Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2007, Article ID 85737, 14 pages
http://dx.doi.org/10.1155/2007/85737
Research Article

Isomorphisms and Derivations in Lie C*-Algebras

1Department of Mathematics, Hanyang University, Seoul 133–791, South Korea
2Department of Mathematics Education, Pusan National University, Pusan 609–735, South Korea
3Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received 7 May 2007; Revised 10 July 2007; Accepted 13 July 2007

Academic Editor: John Michael Rassias

Copyright © 2007 Choonkil Park 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, A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, no. 8, Interscience, New York, NY, USA, 1960. View at Zentralblatt MATH · View at MathSciNet
  2. D. H. Hyers, “On the stability of the linear functional equation,” Proceedings of the National Academy of Sciences of the United States of America, vol. 27, no. 4, pp. 222–224, 1941. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. Th. M. Rassias, “On the stability of the linear mapping in Banach spaces,” Proceedings of the American Mathematical Society, vol. 72, no. 2, pp. 297–300, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. P. Găvruta, “A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings,” Journal of Mathematical Analysis and Applications, vol. 184, no. 3, pp. 431–436, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. C. Baak, “Cauchy-Rassias stability of Cauchy-Jensen additive mappings in Banach spaces,” Acta Mathematica Sinica, vol. 22, no. 6, pp. 1789–1796, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  6. C.-G. Park, “Lie -homomorphisms between Lie C-algebras and Lie -derivations on Lie C-algebras,” Journal of Mathematical Analysis and Applications, vol. 293, no. 2, pp. 419–434, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. C.-G. Park, “Homomorphisms between Lie JC-algebras and Cauchy-Rassias stability of Lie JC-algebra derivations,” Journal of Lie Theory, vol. 15, no. 2, pp. 393–414, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. C.-G. Park, “Homomorphisms between Poisson JC-algebras,” Bulletin of the Brazilian Mathematical Society, vol. 36, no. 1, pp. 79–97, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. C. Park, “Stability of an Euler-Lagrange-Rassias type additive mapping,” International Journal of Applied Mathematics & Statistics, vol. 7, no. Fe07, pp. 101–111, 2007. View at Google Scholar
  10. C. Park, “Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras,” to appear in Bulletin des Sciences Mathématiques.
  11. C. Park, Y. S. Cho, and M.-H. Han, “Functional inequalities associated with Jordan-von Neumann-type additive functional equations,” Journal of Inequalities and Applications, vol. 2007, Article ID 41820, 13 pages, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  12. C. Park and J. Cui, “Generalized stability of C-ternary quadratic mappings,” Abstract and Applied Analysis, vol. 2007, Article ID 23282, 6 pages, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  13. C. G. Park, J. C. Hou, and S. Q. Oh, “Homomorphisms between JC-algebras and Lie C-algebras,” Acta Mathematica Sinica, vol. 21, no. 6, pp. 1391–1398, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  14. C. Park and A. Najati, “Homomorphisms and derivations in C-algebras,” Abstract and Applied Analysis, vol. 2007, Article ID 80630, 12 pages, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  15. J. M. Rassias, “On approximation of approximately linear mappings by linear mappings,” Journal of Functional Analysis, vol. 46, no. 1, pp. 126–130, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. P. Găvruta, “An answer to a question of John M. Rassias concerning the stability of Cauchy equation,” in Advances in Equations and Inequalities, Hadronic Math. Ser., pp. 67–71, Hadronic Press, Palm Harbor, Fla, USA, 1999. View at Google Scholar
  17. M. A. Sibaha, B. Bouikhalene, and E. Elqorachi, “Ulam-Găvruta-Rassias stability for a linear functional equation,” International Journal of Applied Mathematics & Statistics, vol. 7, no. Fe07, pp. 157–168, 2007. View at Google Scholar
  18. K. Ravi and M. Arunkumar, “On the Ulam-Găvruta-Rassias stability of the orthogonally Euler-Lagrange type functional equation,” International Journal of Applied Mathematics & Statistics, vol. 7, no. Fe07, pp. 143–156, 2007. View at Google Scholar
  19. J. M. Rassias, “On the stability of the Euler-Lagrange functional equation,” Chinese Journal of Mathematics, vol. 20, no. 2, pp. 185–190, 1992. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. J. M. Rassias, “On the stability of the non-linear Euler-Lagrange functional equation in real normed linear spaces,” Journal of Mathematical and Physical Sciences, vol. 28, no. 5, pp. 231–235, 1994. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. J. M. Rassias, “On the stability of the general Euler-Lagrange functional equation,” Demonstratio Mathematica, vol. 29, no. 4, pp. 755–766, 1996. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. J. M. Rassias, “Solution of the Ulam stability problem for Euler-Lagrange quadratic mappings,” Journal of Mathematical Analysis and Applications, vol. 220, no. 2, pp. 613–639, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. J. M. Rassias, “On the stability of the multi-dimensional Euler-Lagrange functional equation,” The Journal of the Indian Mathematical Society, vol. 66, no. 1–4, pp. 1–9, 1999. View at Google Scholar · View at MathSciNet
  24. J. M. Rassias, “Asymptotic behavior of mixed type functional equations,” The Australian Journal of Mathematical Analysis and Applications, vol. 1, no. 1, article 10, pp. 1–21, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. M. J. Rassias and J. M. Rassias, “On the Ulam stability for Euler-Lagrange type quadratic functional equations,” The Australian Journal of Mathematical Analysis and Applications, vol. 2, no. 1, article 11, pp. 1–10, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. J. M. Rassias, “On approximation of approximately linear mappings by linear mappings,” Bulletin des Sciences Mathématiques, vol. 108, no. 4, pp. 445–446, 1984. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. J. M. Rassias, “Solution of a problem of Ulam,” Journal of Approximation Theory, vol. 57, no. 3, pp. 268–273, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. J. M. Rassias, “Solution of a stability problem of Ulam,” Discussiones Mathematicae, vol. 12, pp. 95–103, 1992. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. J. M. Rassias, “Complete solution of the multi-dimensional problem of Ulam,” Discussiones Mathematicae, vol. 14, pp. 101–107, 1994. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. J. M. Rassias, “Alternative contraction principle and Ulam stability problem,” Mathematical Sciences Research Journal, vol. 9, no. 7, pp. 190–199, 2005. View at Google Scholar · View at MathSciNet
  31. J. M. Rassias, “Solution of the Hyers-Ulam stability problem for quadratic type functional equations in several variables,” The Australian Journal of Mathematical Analysis and Applications, vol. 2, no. 2, article 11, pp. 1–9, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. J. M. Rassias, “On the general quadratic functional equation,” Boletín de la Sociedad Matemática Mexicana, vol. 11, no. 2, pp. 259–268, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. J. M. Rassias, “On the Ulam problem for Euler quadratic mappings,” Novi Sad Journal of Mathematics, vol. 35, no. 2, pp. 57–66, 2005. View at Google Scholar · View at MathSciNet
  34. J. M. Rassias, “On the Cauchy-Ulam stability of the Jensen equation in C-algebras,” International Journal of Pure and Applied Mathematical Sciences, vol. 2, no. 1, pp. 92–101, 2005. View at Google Scholar
  35. J. M. Rassias, “Alternative contraction principle and alternative Jensen and Jensen type mappings,” International Journal of Applied Mathematics & Statistics, vol. 4, no. M06, pp. 1–10, 2006. View at Google Scholar · View at MathSciNet
  36. J. M. Rassias, “Refined Hyers-Ulam approximation of approximately Jensen type mappings,” Bulletin des Sciences Mathématiques, vol. 131, no. 1, pp. 89–98, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  37. J. M. Rassias and M. J. Rassias, “On some approximately quadratic mappings being exactly quadratic,” The Journal of the Indian Mathematical Society, vol. 69, no. 1–4, pp. 155–160, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  38. J. M. Rassias and M. J. Rassias, “Asymptotic behavior of Jensen and Jensen type functional equations,” Pan-American Mathematical Journal, vol. 15, no. 4, pp. 21–35, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  39. J. M. Rassias and M. J. Rassias, “Asymptotic behavior of alternative Jensen and Jensen type functional equations,” Bulletin des Sciences Mathématiques, vol. 129, no. 7, pp. 545–558, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  40. Th. M. Rassias, “The problem of S. M. Ulam for approximately multiplicative mappings,” Journal of Mathematical Analysis and Applications, vol. 246, no. 2, pp. 352–378, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  41. Th. M. Rassias, “On the stability of functional equations in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 251, no. 1, pp. 264–284, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  42. Th. M. Rassias, “On the stability of functional equations and a problem of Ulam,” Acta Applicandae Mathematicae, vol. 62, no. 1, pp. 23–130, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  43. Th. M. Rassias, Ed., Functional Equations, Inequalities and Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2003. View at Zentralblatt MATH · View at MathSciNet
  44. F. Skof, “Proprietà locali e approssimazione di operatori,” Rendiconti del Seminario Matematico e Fisico di Milano, vol. 53, pp. 113–129, 1983. View at Google Scholar
  45. A. Gilányi, “Eine zur Parallelogrammgleichung äquivalente Ungleichung,” Aequationes Mathematicae, vol. 62, no. 3, pp. 303–309, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  46. J. Rätz, “On inequalities associated with the Jordan-von Neumann functional equation,” Aequationes Mathematicae, vol. 66, no. 1-2, pp. 191–200, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  47. W. Fechner, “Stability of a functional inequality associated with the Jordan-von Neumann functional equation,” Aequationes Mathematicae, vol. 71, no. 1-2, pp. 149–161, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  48. A. Gilányi, “On a problem by K. Nikodem,” Mathematical Inequalities & Applications, vol. 5, no. 4, pp. 707–710, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet