Acta Mathematica Hungarica

, Volume 134, Issue 1–2, pp 99–114

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

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

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 equation fixed point homomorphism in multi-C ternary algebra generalized Hyers–Ulam stability derivation on multi-C ternary algebra multi-normed space 

2000 Mathematics Subject Classification

39A10 39B72 47H10 46B03 

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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

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