Document Type : Research Paper

Authors

• E. Elqorachi ¹
• Y. Manar ¹
• Th. M. Rassias ²

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

• Hyers-Ulam-Rassias stability
• quadratic functional equation