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Functional Equations Related to Inner Product Spaces

Author

Listed:
  • Choonkil Park
  • Won-Gil Park
  • Abbas Najati

Abstract

Let V, W be real vector spaces. It is shown that an odd mapping f : V → W satisfies ∑i−12nf(xi−1/2n∑j=12nxj)=∑i=12nf(xi)−2nf(1/2n∑i=12nxi) for all x1, …, x2n ∈ V if and only if the odd mapping f : V → W is Cauchy additive. Furthermore, we prove the generalized Hyers‐Ulam stability of the above functional equation in real Banach spaces.

Suggested Citation

  • Choonkil Park & Won-Gil Park & Abbas Najati, 2009. "Functional Equations Related to Inner Product Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    • Handle: RePEc:wly:jnlaaa:v:2009:y:2009:i:1:n:907121
    DOI: 10.1155/2009/907121
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    References listed on IDEAS

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    1. Paisan Nakmahachalasint, 2007. "On the Generalized Ulam-Gavruta-Rassias Stability of Mixed-Type Linear and Euler-Lagrange-Rassias Functional Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2007, pages 1-10, May.
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    Cited by:

    1. Zhihua Wang & Themistocles M. Rassias, 2011. "Intuitionistic Fuzzy Stability of Functional Equations Associated with Inner Product Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).

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