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

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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

$$\sum_{i=1}^{m}f \bigg(mx_i+\sum_{j=1,\ j\ne i}^{m}x_j\bigg)+ f\bigg(\sum_{i=1}^{m}x_i\bigg)= 2f\bigg(\sum_{i=1}^{m}mx_i\bigg) \quad (m\in {\mathbb{N}},\ m\geqq2).$$

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Authors and Affiliations

  1. Department of Mathematics, National University of Ireland, Galway, Ireland

    Donal O’Regan

  2. Section of Mathematics and Informatics, Pedagogical Department, National and Capodistrian University of Athens, 4, Agamemnonos St., Aghia Paraskevi, Athens, 15342, Greece

    John Michael Rassias

  3. Department of Mathematics, Science and Research Branch, Islamic Azad University, Post Code 14778, Ashrafi Esfahani Ave, Tehran, I.R. Iran

    Reza Saadati

Authors
  1. Donal O’Regan
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  2. John Michael Rassias
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  3. Reza Saadati
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Correspondence to Reza Saadati.

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O’Regan, D., Rassias, J.M. & Saadati, R. Approximations of ternary Jordan homomorphisms and derivations in multi-C ∗ ternary algebras. Acta Math Hung 134, 99–114 (2012). https://doi.org/10.1007/s10474-011-0116-0

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  • DOI: https://doi.org/10.1007/s10474-011-0116-0

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