- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 684179, 12 pages
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.
- S. M. Ulam, Problems in Modern Mathematics, chapter 10, John Wiley & Sons, New York, NY ,USA, 1940.
- 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.
- D. G. Bourgin, “Classes of transformations and bordering transformations,” Bulletin of the American Mathematical Society, vol. 57, pp. 223–237, 1951.
- 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.
- 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.
- 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.
- 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.
- 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.
- A. Fošner, “On the generalized Hyers-Ulam stability of module left (m, n)- derivations,” Aequations Mathematicae, in press.
- D. H. Hyers, G. Isac, and T. M. Rassias, Stability of Functional Equations in Several Variables, Birkhäuser, Boston, Mass, USA, 1998.
- M. S. Moslehian, “Ternary derivations, stability and physical aspects,” Acta Applicandae Mathematicae, vol. 100, no. 2, pp. 187–199, 2008.
- S. Y. Jang and C. Park, “Approximate ∗-derivations and approximate quadratic ∗-derivations on -algebras,” Journal of Inequalities and Applications, vol. 2011, p. 55, 2011.
- 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.
- 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.
- A. Bodaghi and I. A. Alias, “Approximate ternary quadratic derivations on ternary Banach algebras and -ternary rings,” Advances in Difference Equations, vol. 2012, p. 11, 2012.
- 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.
- M. Eshaghi Gordji and A. Najati, “Approximately -homomorphisms: a fixed point approach,” Journal of Geometry and Physics, vol. 60, no. 5, pp. 809–814, 2010.
- 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.
- 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.
- M. Eshaghi Gordji, S. Kaboli Gharetapeh, M. Bodkham, T. Karimi, and M. Aghaei, “Almost homomorhismbetween unital -algebras: a fixed point approch,” Analysis in Theory and Applications, vol. 27, no. 4, pp. 320–331, 2011.
- C.-G. Park and J. Hou, “Homomorphisms between -algebras associated with the Trif functional equation and linear derivations on -algebras,” Journal of the Korean Mathematical Society, vol. 41, no. 3, pp. 461–477, 2004.
- 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.
- M. Turinici, “Sequentially iterative processes and applications to Volterra functional equations,” Annales Universitatis Mariae Curie Skłodowska A, vol. 32, pp. 127–134, 1978.
- 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.