Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68221220100801stability of the quadratic functional equation26357210.22075/ijnaa.2010.72ENE.ElqorachiDepartment of Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir, MoroccoY.ManarDepartment of Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir, MoroccoTh. M.RassiasDepartment of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, GreeceJournal Article20100212In the present paper a solution of the generalized quadratic functional equation<br />$$<br />f(kx+ y)+f(kx+\sigma(y))=2k^{2}f(x)+2f(y),\phantom{+} x,y\in{E}$$<br />is given where $\sigma$ is an involution of the normed space $E$ and $k$ is a fixed positive integer. Furthermore we investigate the Hyers-Ulam-Rassias stability of the functional equation. The Hyers-Ulam stability on unbounded domains is also studied. Applications of the results for the asymptotic behavior of the generalized quadratic functional equation are provided.https://ijnaa.semnan.ac.ir/article_72_80bd73337686e609bb56f0fac56e6130.pdf