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Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non‐Archimedean Normed Spaces

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  • Abasalt Bodaghi
  • Sang Og Kim

Abstract

We obtain the general solution of the generalized mixed additive and quadratic functional equation f(x + my) + f(x − my) = 2f(x) − 2m2f(y) + m2f(2y), m is even; f(x + y) + f(x − y) − 2(m2 − 1)f(y) + (m2 − 1)f(2y), m is odd, for a positive integer m. We establish the Hyers‐Ulam stability for these functional equations in non‐Archimedean normed spaces when m is an even positive integer or m = 3.

Suggested Citation

  • Abasalt Bodaghi & Sang Og Kim, 2013. "Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non‐Archimedean Normed Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:198018
    DOI: 10.1155/2013/198018
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    References listed on IDEAS

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    1. Soon-Mo Jung, 2011. "Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis," Springer Optimization and Its Applications, Springer, number 978-1-4419-9637-4, January.
    2. Jung Rye Lee & Jong Su An & Choonkil Park, 2008. "On the Stability of Quadratic Functional Equations," Abstract and Applied Analysis, Hindawi, vol. 2008, pages 1-8, March.
    3. 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).
    4. Jung Rye Lee & Jong Su An & Choonkil Park, 2008. "On the Stability of Quadratic Functional Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2008(1).
    5. 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.
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    Cited by:

    1. Abasalt Bodaghi, 2025. "Estimation of Inexact Multimixed Additive‐Quadratic Mappings in Fuzzy Normed Spaces," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).

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