Mediterranean Journal of Mathematics

, Volume 6, Issue 2, pp 233–248 | Cite as

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

  • Fridoun Moradlou
  • Hamid Vaezi
  • G. Zamani Eskandani


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.

Mathematics Subject Classification (2000)

Primary 39B52 Secondary 39B72 47Jxx 


Hyers–Ulam–Rassias stability quadratic function additive function quasi-Banach space p-Banach space 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Fridoun Moradlou
    • 1
  • Hamid Vaezi
    • 2
  • G. Zamani Eskandani
    • 2
  1. 1.Department of MathematicsSahand University of TechnologyTabrizIran
  2. 2.Faculty of Mathematical SciencesUniversity of TabrizTabrizIran

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