Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68221220100601stability 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 Article20131102In the present paper a solution of the generalized<br />quadratic functional equation<br />$$<br />f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ is<br />given where $sigma$ is an involution of the normed space $E$ and<br />$k$ is a fixed positive integer. Furthermore we investigate the<br />Hyers-Ulam-Rassias stability of the functional equation. The<br />Hyers-Ulam stability on unbounded domains is also studied.<br />Applications of the results for the asymptotic behavior of the<br />generalized quadratic functional equation are provided.https://ijnaa.semnan.ac.ir/article_72_80bd73337686e609bb56f0fac56e6130.pdf