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Mediterranean Journal of Mathematics

, Volume 8, Issue 3, pp 331–348 | Cite as

Generalized Hyers-Ulam Stability for a General Mixed Functional Equation in Quasi-β-normed Spaces

  • G. Zamani Eskandani
  • Pasc Gavruta
  • John M. Rassias
  • Ramazan Zarghami
Article

Abstract

In this paper, we establish the general solution and investigate the generalized Hyers-Ulam stability of the following mixed additive and quadratic functional equation
$$f(\lambda x + y) + f(\lambda x - y) = f(x + y) + f(x - y) + (\lambda - 1)[(\lambda +2)f(x) + \lambda f(-x)],$$
\({(\lambda \in {\mathbb N}, \lambda \ne 1)}\) in quasi-β-normed spaces.

Mathematics Subject Classification (2010)

39B72 39B82 46B03 47Jxx 

Keywords

Generalized Hyers-Ulam stability Contractively subadditive Expansively superadditive quasi-β-normed space (β, p)-Banach space 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • G. Zamani Eskandani
    • 1
  • Pasc Gavruta
    • 2
  • John M. Rassias
    • 3
  • Ramazan Zarghami
    • 1
  1. 1.Faculty of Sciences, Department of MathematicsUniversity of TabrizTabrizIran
  2. 2.Department of MathematicsUniversity “Politehnica” of TimisoaraTimisoaraRomania
  3. 3.Pedagogical Department E.E.National and Capodistrian University of AthensAthensGreece

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