Abstract and Applied Analysis

Approximately Ternary Homomorphisms and Derivations on C -Ternary Algebras

M. Eshaghi Gordji, A. Ebadian, N. Ghobadipour, J. M. Rassias, and M. B. Savadkouhi

Full-text: Open access


We investigate the stability and superstability of ternary homomorphisms between C {\ast} -ternary algebras and derivations on C {\ast} -ternary algebras, associated with the following functional equation f ( ( x 2 - x 1 ) / 3 ) + f ( ( x 1 - 3 x 3 ) / 3 ) + f ( ( 3 x 1 + 3 x 3 - x 2 ) / 3 ) = f ( x 1 ) .

Article information

Abstr. Appl. Anal., Volume 2012 (2012), Article ID 984160, 10 pages.

First available in Project Euclid: 14 December 2012

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Gordji, M. Eshaghi; Ebadian, A.; Ghobadipour, N.; Rassias, J. M.; Savadkouhi, M. B. Approximately Ternary Homomorphisms and Derivations on ${C}^{{\ast} }$ -Ternary Algebras. Abstr. Appl. Anal. 2012 (2012), Article ID 984160, 10 pages. doi:10.1155/2012/984160. https://projecteuclid.org/euclid.aaa/1355495675

Export citation


  • F. Bagarello and G. Morchio, “Dynamics of mean-field spin models from basic results in abstract differential equations,” Journal of Statistical Physics, vol. 66, no. 3-4, pp. 849–866, 1992.
  • N. Bazunova, A. Borowiec, and R. Kerner, “Universal differential calculus on ternary algebras,” Letters in Mathematical Physics, vol. 67, no. 3, pp. 195–206, 2004.
  • M. B. Savadkouhi, M. E. Gordji, J. M. Rassias, and N. Ghobadipour, “Approximate ternary Jordan derivations on Banach ternary algebras,” Journal of Mathematical Physics, vol. 50, no. 4, Article ID 042303, 9 pages, 2009.
  • A. Ebadian, N. Ghobadipour, and M. Eshaghi Gordji, “A fixed point method for perturbation of bi-multipliers and Jordan bimultipliers in ${C}^{\ast\,\!}$-ternary algebras,” Journal of Mathematical Physics, vol. 51, no. 10, Article ID 103508, 2010.
  • M. E. Gordji, R. Khodabakhsh, and H. Khodaei, “On approximate n-ary derivations,” International Journal of Geometric Methods in Modern Physics, vol. 8, no. 3, pp. 485–500, 2011.
  • L. Vainerman and R. Kerner, “On special classes of n-algebras,” Journal of Mathematical Physics, vol. 37, no. 5, pp. 2553–2565, 1996.
  • S. M. Ulam, Problems in Modern Mathematics, John Wiley & Sons, New York, NY, USA, 1940.
  • Th. M. Rassias and J. Tabor, “What is left of Hyers-Ulam stability?” Journal of Natural Geometry, vol. 1, no. 2, pp. 65–69, 1992.
  • G. L. Sewell, Quantum Mechanics and Its Emergent Macrophysics, Princeton University Press, Princeton, NJ, USA, 2002.
  • 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. M. Rassias, “On the stability of minimum points,” Mathematica, vol. 45(68), no. 1, pp. 93–104, 2003.
  • R. Kerner, “The cubic chessboard,” Classical and Quantum Gravity, vol. 14, no. 1A, pp. A203–A225, 1997.
  • 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.
  • A. Ebadian, S. Kaboli Gharetapeh, and M. Eshaghi Gordji, “Nearly Jordan $\ast\,\!$-homomorphisms between unital ${C}^{\ast\,\!}$-algebras,” Abstract and Applied Analysis, vol. 2011, Article ID 513128, 12 pages, 2011.
  • A. Ebadian, A. Najati, and M. Eshaghi Gordji, “On approximate additive-quartic and quadratic-cubic functional equations in two variables on abelian groups,” Results in Mathematics, vol. 58, no. 1-2, pp. 39–53, 2010.
  • M. Eshaghi Gordji, M. B. Ghaemi, S. Kaboli Gharetapeh, S. Shams, and A. Ebadian, “On the stability of ${J}^{\ast\,\!}$-derivations,” Journal of Geometry and Physics, vol. 60, no. 3, pp. 454–459, 2010.
  • M. E. Gordji, N. Ghobadipour, and C. Park, “Jordan $\ast\,\!$-homomorphisms on ${C}^{\ast\,\!}$-algebras,” Operators and Matrices, vol. 5, no. 3, pp. 541–551, 2011.
  • M. E. Gordji and N. Ghobadipour, “Stability of ($\alpha $, $\beta $, $\gamma $)-derivations on Lie ${C}^{\ast\,\!}$-algebras,” International Journal of Geometric Methods in Modern Physics, vol. 7, no. 7, pp. 1093–1102, 2010.
  • M. Eshaghi Gordji and A. Najati, “Approximately ${J}^{\ast\,\!}$-homomorphisms: a fixed point approach,” Journal of Geometry and Physics, vol. 60, no. 5, pp. 809–814, 2010.
  • D. H. Hyers, G. Isac, and T. M. Rassias, Stability of Functional Equations in Several Variables, Progress in Nonlinear Differential Equations and their Applications, 34, Birkhäuser, Boston, Mass, USA, 1998.
  • D. H. Hyers and T. M. Rassias, “Approximate homomorphisms,” Aequationes Mathematicae, vol. 44, no. 2-3, pp. 125–153, 1992.
  • G. Isac and T. M. Rassias, “On the Hyers-Ulam stability of $\psi $-additive mappings,” Journal of Approxima-tion Theory, vol. 72, no. 2, pp. 131–137, 1993.
  • G. Isac and T. M. Rassias, “Stability of $\psi $-additive mappings: applications to nonlinear analysis,” Inter-national Journal of Mathematics and Mathematical Sciences, vol. 19, no. 2, pp. 219–228, 1996.
  • Th. M. Rassias, Ed., Functional Equations and Inequalities, vol. 518 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000.
  • T. M. Rassias, “On the stability of functional equations and a problem of Ulam,” Acta Applicandae Ma-thematicae, vol. 62, no. 1, pp. 23–130, 2000.
  • Th. M. Rassias, “On the stability of the quadratic functional equation and its applications,” Studia Uni-versitatis Babeş-Bolyai. Mathematica, vol. 43, no. 3, pp. 89–124, 1998.
  • 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.
  • M. Eshaghi Gordji, “Nearly involutions on čommentComment on ref. [7?]: Please update the information of this reference, if possible. Banach algebras; A fixed point approach,” to appear in Fix-ed Point Theory.