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Solution and stability of generalized mixed type additive and quadratic functional equation in non-Archimedean spaces

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Abstract

In this paper, we achieve the general solution and the generalized Hyres–Ulam–Rassias stability of the following additive–quadratic functional equation

$$f (x + ky) + f (x - ky) = f (x + y) + f (x - y) + \frac{2(k + 1)}{k} f (ky) - 2(k + 1)f (y)$$

for fixed integers k with k ≠ 0, ±1 in non-Archimedean spaces.

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Authors and Affiliations

  1. Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran

    M. Eshaghi Gordji

  2. Department of Mathematics, Urmia University, Urmia, Iran

    S. Zolfaghari, S. Kaboli Gharetapeh & A. Ebadian

  3. Department of Mathematics, Hanyang University, Seoul, 133-791, Republic of Korea

    C. Park

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  1. M. Eshaghi Gordji
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  2. S. Zolfaghari
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  3. S. Kaboli Gharetapeh
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  4. A. Ebadian
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  5. C. Park
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Correspondence to M. Eshaghi Gordji.

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Eshaghi Gordji, M., Zolfaghari, S., Kaboli Gharetapeh, S. et al. Solution and stability of generalized mixed type additive and quadratic functional equation in non-Archimedean spaces. Ann Univ Ferrara 58, 49–64 (2012). https://doi.org/10.1007/s11565-011-0138-0

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