stability of the quadratic functional equation

Authors

1 Department of Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir, Morocco

2 Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens Greece

Abstract

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.

Keywords