About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 684179, 12 pages
http://dx.doi.org/10.1155/2012/684179
Research Article

Approximate Cubic ∗-Derivations on Banach ∗-Algebras

1Department of Mathematics, Hanyang University, Seoul 133-791, Republic of Korea
2Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran
3Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Malaysia

Received 30 March 2012; Revised 2 June 2012; Accepted 16 June 2012

Academic Editor: Janusz Brzdek

Copyright © 2012 Seo Yoon Yang 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 10, John Wiley & Sons, New York, NY ,USA, 1940.
  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, pp. 222–224, 1941. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. D. G. Bourgin, “Classes of transformations and bordering transformations,” Bulletin of the American Mathematical Society, vol. 57, pp. 223–237, 1951. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. T. Aoki, “On 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 · View at Google Scholar · View at Zentralblatt MATH
  5. T. 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
  6. P. Găvruţa, “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
  7. A. Bodaghi, I. A. Alias, and M. H. Ghahramani, “Ulam stability of a quartic functional equation,” Abstract and Applied Analysis, vol. 2012, Article ID 232630, 9 pages, 2012. View at Publisher · View at Google Scholar
  8. M. Eshaghi Gordji and A. Bodaghi, “On the Hyers-Ulam-Rassias stability problem for quadratic functional equations,” East Journal on Approximations, vol. 16, no. 2, pp. 123–130, 2010.
  9. A. Fošner, “On the generalized Hyers-Ulam stability of module left (m, n)- derivations,” Aequations Mathematicae, in press. View at Publisher · View at Google Scholar
  10. D. H. Hyers, G. Isac, and T. M. Rassias, Stability of Functional Equations in Several Variables, Birkhäuser, Boston, Mass, USA, 1998. View at Publisher · View at Google Scholar
  11. M. S. Moslehian, “Ternary derivations, stability and physical aspects,” Acta Applicandae Mathematicae, vol. 100, no. 2, pp. 187–199, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. S. Y. Jang and C. Park, “Approximate -derivations and approximate quadratic -derivations on C-algebras,” Journal of Inequalities and Applications, vol. 2011, p. 55, 2011.
  13. L. Cǎdariu and V. Radu, “On the stability of the Cauchy functional equation: a fixed point approach,” Grazer Mathematische Berichte, vol. 346, pp. 43–52, 2004.
  14. L. Cǎdariu and V. Radu, “Fixed points and the stability of quadratic functional equations,” Analele Universitatii de Vest din Timisoara, vol. 41, no. 1, pp. 25–48, 2003.
  15. A. Bodaghi and I. A. Alias, “Approximate ternary quadratic derivations on ternary Banach algebras and C-ternary rings,” Advances in Difference Equations, vol. 2012, p. 11, 2012. View at Publisher · View at Google Scholar
  16. M. Eshaghi Gordji, A. Bodaghi, and C. Park, “A fixed point approach to the stability of double Jordan centralizers and Jordan multipliers on Banach algebras,” Scientific Bulletin A, vol. 73, no. 2, pp. 65–74, 2011.
  17. M. Eshaghi Gordji and A. Najati, “Approximately J-homomorphisms: a fixed point approach,” Journal of Geometry and Physics, vol. 60, no. 5, pp. 809–814, 2010. View at Publisher · View at Google Scholar
  18. C. Park, “Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras,” Fixed Point Theory and Applications, vol. 2007, Article ID 50175, 15 pages, 2007. View at Zentralblatt MATH
  19. A. Bodaghi, I. A. Alias, and M. H. Ghahramani, “Approximately cubic functional equations and cubic multipliers,” Journal of Inequalities and Applications, vol. 2011, p. 53, 2011. View at Publisher · View at Google Scholar
  20. M. Eshaghi Gordji, S. Kaboli Gharetapeh, M. Bodkham, T. Karimi, and M. Aghaei, “Almost homomorhismbetween unital C-algebras: a fixed point approch,” Analysis in Theory and Applications, vol. 27, no. 4, pp. 320–331, 2011. View at Publisher · View at Google Scholar
  21. C.-G. Park and J. Hou, “Homomorphisms between C-algebras associated with the Trif functional equation and linear derivations on C-algebras,” Journal of the Korean Mathematical Society, vol. 41, no. 3, pp. 461–477, 2004. View at Publisher · View at Google Scholar
  22. M. Eshaghi Gordji, S. Kaboli Gharetapeh, M. B. Savadkouhi, M. Aghaei, and T. Karimi, “On cubic derivations,” International Journal of Mathematical Analysis, vol. 4, no. 49-52, pp. 2501–2514, 2010. View at Zentralblatt MATH
  23. M. Turinici, “Sequentially iterative processes and applications to Volterra functional equations,” Annales Universitatis Mariae Curie Skłodowska A, vol. 32, pp. 127–134, 1978. View at Zentralblatt MATH
  24. J. B. Diaz and B. Margolis, “A fixed point theorem of the alternative, for contractions on a generalized complete metric space,” Bulletin of the American Mathematical Society, vol. 74, pp. 305–309, 1968. View at Publisher · View at Google Scholar · View at Zentralblatt MATH