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.
Elqorachi, E., Manar, Y., Rassias, T. (2010). stability of the quadratic functional
equation. International Journal of Nonlinear Analysis and Applications, 1(2), 26-35. doi: 10.22075/ijnaa.2010.72
MLA
E. Elqorachi; Y. Manar; Th. M. Rassias. "stability of the quadratic functional
equation". International Journal of Nonlinear Analysis and Applications, 1, 2, 2010, 26-35. doi: 10.22075/ijnaa.2010.72
HARVARD
Elqorachi, E., Manar, Y., Rassias, T. (2010). 'stability of the quadratic functional
equation', International Journal of Nonlinear Analysis and Applications, 1(2), pp. 26-35. doi: 10.22075/ijnaa.2010.72
VANCOUVER
Elqorachi, E., Manar, Y., Rassias, T. stability of the quadratic functional
equation. International Journal of Nonlinear Analysis and Applications, 2010; 1(2): 26-35. doi: 10.22075/ijnaa.2010.72
)