Acta Mathematica Hungarica

, Volume 134, Issue 1, pp 99–114

Approximations of ternary Jordan homomorphisms and derivations in multi-C ternary algebras

  • Donal O’Regan
  • John Michael Rassias
  • Reza Saadati
Article

DOI: 10.1007/s10474-011-0116-0

Cite this article as:
O’Regan, D., Rassias, J.M. & Saadati, R. Acta Math Hung (2012) 134: 99. doi:10.1007/s10474-011-0116-0

Abstract

Using fixed point methods, we prove the generalized Hyers–Ulam stability of homomorphisms in multi-C ternary algebras and of derivations on multi-C ternary algebras for the additive functional equation
$$\sum_{i=1}^{m}f \bigg(mx_i+\sum_{j=1,\ j\ne i}^{m}x_j\bigg)+ f\bigg(\sum_{i=1}^{m}x_i\bigg)= 2f\bigg(\sum_{i=1}^{m}mx_i\bigg) \quad (m\in {\mathbb{N}},\ m\geqq2).$$

Key words and phrases

additive functional equationfixed pointhomomorphism in multi-C ternary algebrageneralized Hyers–Ulam stabilityderivation on multi-C ternary algebramulti-normed space

2000 Mathematics Subject Classification

39A1039B7247H1046B03

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2011

Authors and Affiliations

  • Donal O’Regan
    • 1
  • John Michael Rassias
    • 2
  • Reza Saadati
    • 3
  1. 1.Department of MathematicsNational University of IrelandGalwayIreland
  2. 2.Section of Mathematics and Informatics, Pedagogical DepartmentNational and Capodistrian University of AthensAthensGreece
  3. 3.Department of Mathematics, Science and Research BranchIslamic Azad UniversityTehranI.R. Iran