- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 425784, 5 pages
Approximate Cubic Lie Derivations
1Faculty of Management, University of Primorska, Cankarjeva 5, 6104 Koper, Slovenia
2Faculty of Logistics, University of Maribor, Mariborska Cesta 7, 3000 Celje, Slovenia
Received 11 April 2013; Accepted 27 June 2013
Academic Editor: Janusz Brzdek
Copyright © 2013 Ajda Fošner and Maja Fošner. 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, John Wiley & Sons, New York, NY, USA, 1964.
- 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.
- 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.
- D. H. Hyers, G. Isac, and T. M. Rassias, Stability of Functional Equations in Several Variables, Birkhäuser, Boston, Mass, USA, 1998.
- S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, vol. 48 of Springer Optimization and Its Applications, Springer, New York, NY, USA, 2011.
- K.-W. Jun and H.-M. Kim, “The generalized Hyers-Ulam-Rassias stability of a cubic functional equation,” Journal of Mathematical Analysis and Applications, vol. 274, no. 2, pp. 267–278, 2002.
- A. Bodaghi, I. A. Alias, and M. H. Ghahramani, “Approximately cubic functional equations and cubic multipliers,” Journal of Inequalities and Applications, vol. 2011, articlie 53, 2011.
- M. E. Gordji, S. K. Gharetapeh, J. M. Rassias, and S. Zolfaghari, “Solution and stability of a mixed type additive, quadratic, and cubic functional equation,” Advances in Difference Equations, vol. 2009, pp. 1–17, 2009.
- M. Eshaghi Gordji, S. Zolfaghari, J. M. Rassias, and M. B. Savadkouhi, “Solution and stability of a mixed type cubic and quartic functional equation in quasi-Banach spaces,” Abstract and Applied Analysis, vol. 2009, Article ID 417473, 14 pages, 2009.
- K.-W. Jun, H.-M. Kim, and I.-S. Chang, “On the Hyers-Ulam stability of an Euler-Lagrange type cubic functional equation,” Journal of Computational Analysis and Applications, vol. 7, no. 1, pp. 21–33, 2005.
- A. Najati, “Hyers-Ulam-Rassias stability of a cubic functional equation,” Bulletin of the Korean Mathematical Society, vol. 44, no. 4, pp. 825–840, 2007.
- T. Z. Xu, J. M. Rassias, and W. X. Xu, “A generalized mixed type of quartic-cubic-quadratic-additive functional equations,” Ukrainian Mathematical Journal, vol. 63, no. 3, pp. 461–479, 2011.
- 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.
- S. Y. Yang, A. Bodaghi, and K. A. M. Atan, “Approximate cubic *-derivations on Banach *-algebras,” Abstract and Applied Analysis, vol. 2012, Article ID 684179, 12 pages, 2012.
- B. Hayati, M. E. Gordji, M. B. Savadkouhi, and M. Bidkham, “Stability of ternary cubic derivations on ternary Frèchet algebras,” Australian Journal of Basic and Applied Sciences, vol. 5, pp. 1224–1235, 2011.
- St. Czerwik, “On the stability of the quadratic mapping in normed spaces,” Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, vol. 62, pp. 59–64, 1992.
- S. Kurepa, “On the quadratic functional,” Publications de l'Institut Mathématique de l'Académie Serbe des. Sciences, vol. 13, pp. 57–72, 1961.
- Z. Moszner, “Sur les définitions différentes de la stabilité des équations fonctionnelles,” Aequationes Mathematicae, vol. 68, no. 3, pp. 260–274, 2004.
- D. G. Bourgin, “Approximately isometric and multiplicative transformations on continuous function rings,” Duke Mathematical Journal, vol. 16, pp. 385–397, 1949.
- G. Maksa and Z. Páles, “Hyperstability of a class of linear functional equations,” Acta Mathematica. Academiae Paedagogicae Nyíregyháziensis, vol. 17, no. 2, pp. 107–112, 2001.
- E. Gselmann, “Hyperstability of a functional equation,” Acta Mathematica Hungarica, vol. 124, no. 1-2, pp. 179–188, 2009.
- Gy. Maksa, K. Nikodem, and Zs. Páles, “Results on -Wright convexity,” L'Académie des Sciences. Comptes Rendus Mathématiques, vol. 13, no. 6, pp. 274–278, 1991.
- N. Brillouët-Belluot, J. Brzdęk, and K. Ciepliński, “On some recent developments in Ulam's type stability,” Abstract and Applied Analysis, vol. 2012, Article ID 716936, 41 pages, 2012.
- J. Brzdȩk, “Hyperstability of the Cauchy equation on restricted domains,” Acta Mathematica Hungarica, 2013.
- M. Piszczek, “Remark on hyperstability of the general linear equation,” Aequationes Mathematicae, 2013.
- A. Najati, “The generalized Hyers-Ulam-Rassias stability of a cubic functional equation,” Turkish Journal of Mathematics, vol. 31, no. 4, pp. 395–408, 2007.