%0 Journal Article
%T stability of the quadratic functional equation
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Elqorachi, E.
%A Manar, Y.
%A Rassias, Th. M.
%D 2010
%\ 08/01/2010
%V 1
%N 2
%P 26-35
%! stability of the quadratic functional equation
%K Hyers-Ulam-Rassias stability
%K quadratic functional equation
%R 10.22075/ijnaa.2010.72
%X In the present paper a solution of the generalized quadratic functional equation$$f(kx+ y)+f(kx+\sigma(y))=2k^{2}f(x)+2f(y),\phantom{+} x,y\in{E}$$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.
%U https://ijnaa.semnan.ac.ir/article_72_80bd73337686e609bb56f0fac56e6130.pdf