stability of the quadratic functional equation

Authors

E. Elqorachi Department of Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir, Morocco

Th. M. Rassias Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens Greece

Y. Manar Department of Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir, Morocco

Abstract:

In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applications of the results for the asymptotic behavior of thegeneralized quadratic functional equation are provided.

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