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Hyers–Ulam–Rassias Stability of a Quadratic and Additive Functional Equation in Quasi-Banach Spaces

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Abstract

In this paper we establish the general solution of the functional equation

$$f(x + 2y) + f(x - 2y) + 4f(x) = 3[f(x + y) + f(x - y)] + f(2y) - 2f(y)$$

and investigate the Hyers–Ulam–Rassias stability of this equation in quasi-Banach spaces. The concept of Hyers–Ulam–Rassias stability originated from Th. M. Rassias’ stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300.

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Authors and Affiliations

  1. Department of Mathematics, Sahand University of Technology, Tabriz, Iran

    Fridoun Moradlou

  2. Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

    Hamid Vaezi & G. Zamani Eskandani

Authors
  1. Fridoun Moradlou
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  2. Hamid Vaezi
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  3. G. Zamani Eskandani
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Correspondence to Hamid Vaezi.

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Moradlou, F., Vaezi, H. & Zamani Eskandani, G. Hyers–Ulam–Rassias Stability of a Quadratic and Additive Functional Equation in Quasi-Banach Spaces. Mediterr. J. Math. 6, 233–248 (2009). https://doi.org/10.1007/s00009-009-0007-6

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  • DOI: https://doi.org/10.1007/s00009-009-0007-6

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