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Stability of a Functional Equation Deriving from Cubic and Quartic Functions

Author

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  • M. Eshaghi Gordji
  • A. Ebadian
  • S. Zolfaghari

Abstract

We obtain the general solution and the generalized Ulam-Hyers stability of the cubic and quartic functional equation 4 ( 𠑓 ( 3 𠑥 + 𠑦 ) + 𠑓 ( 3 𠑥 − 𠑦 ) ) = − 1 2 ( 𠑓 ( 𠑥 + 𠑦 ) + 𠑓 ( 𠑥 − 𠑦 ) ) + 1 2 ( 𠑓 ( 2 𠑥 + 𠑦 ) + 𠑓 ( 2 𠑥 − 𠑦 ) ) − 8 𠑓 ( 𠑦 ) − 1 9 2 𠑓 ( 𠑥 ) + 𠑓 ( 2 𠑦 ) + 3 0 𠑓 ( 2 𠑥 ) .

Suggested Citation

  • M. Eshaghi Gordji & A. Ebadian & S. Zolfaghari, 2008. "Stability of a Functional Equation Deriving from Cubic and Quartic Functions," Abstract and Applied Analysis, Hindawi, vol. 2008, pages 1-17, February.
    • Handle: RePEc:hin:jnlaaa:801904
    DOI: 10.1155/2008/801904
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    Cited by:

    1. M. Eshaghi Gordji & H. Azadi Kenary & H. Rezaei & Y. W. Lee & G. H. Kim, 2012. "Solution and Hyers‐Ulam‐Rassias Stability of Generalized Mixed Type Additive‐Quadratic Functional Equations in Fuzzy Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. M. Bidkham & H. A. Soleiman Mezerji & M. Eshaghi Gordji, 2010. "Hyers‐Ulam Stability of Polynomial Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    3. M. Eshaghi Gordji & M. Kamyar & Th. M. Rassias, 2011. "General Cubic‐Quartic Functional Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    4. M. Eshaghi Gordji & H. Khodaei & A. Ebadian & G. H. Kim, 2012. "Nearly Radical Quadratic Functional Equations in p‐2‐Normed Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. M. Eshaghi Gordji & M. B. Ghaemi & G. H. Kim & Badrkhan Alizadeh, 2011. "Stability and Superstability of Generalized (θ, ϕ)‐Derivations in Non‐Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).

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