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Approximately Ternary Homomorphisms on C*‐Ternary Algebras

Author

Listed:
  • Eon Wha Shim
  • Su Min Kwon
  • Yun Tark Hyen
  • Yong Hun Choi
  • Abasalt Bodaghi

Abstract

Gordji et al. established the Hyers‐Ulam stability and the superstability of C*‐ternary homomorphisms and C*‐ternary derivations on C*‐ternary algebras, associated with the following functional equation: f((x2 − x1)/3) + f((x1 − 3x3)/3) + f((3x1 + 3x3 − x2)/3) = f(x1), by the direct method. Under the conditions in the main theorems, we can show that the related mappings must be zero. In this paper, we correct the conditions and prove the corrected theorems. Furthermore, we prove the Hyers‐Ulam stability and the superstability of C*‐ternary homomorphisms and C*‐ternary derivations on C*‐ternary algebras by using a fixed point approach.

Suggested Citation

  • Eon Wha Shim & Su Min Kwon & Yun Tark Hyen & Yong Hun Choi & Abasalt Bodaghi, 2013. "Approximately Ternary Homomorphisms on C*‐Ternary Algebras," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:734025
    DOI: 10.1155/2013/734025
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    References listed on IDEAS

    as
    1. M. Eshaghi Gordji & M. B. Ghaemi & J. M. Rassias & Badrkhan Alizadeh, 2011. "Nearly Ternary Quadratic Higher Derivations on Non‐Archimedean Ternary Banach Algebras: A Fixed Point Approach," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    2. Abasalt Bodaghi & Idham Arif Alias & Mohammad Hosein Ghahramani, 2012. "Ulam Stability of a Quartic Functional Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Abasalt Bodaghi & Idham Arif Alias & Mohammad Hosein Ghahramani, 2012. "Ulam Stability of a Quartic Functional Equation," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-9, April.
    4. M. Eshaghi Gordji & M. B. Ghaemi & J. M. Rassias & Badrkhan Alizadeh, 2011. "Nearly Ternary Quadratic Higher Derivations on Non-Archimedean Ternary Banach Algebras: A Fixed Point Approach," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-18, November.
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