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 and Rassias,T M . (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
Elqorachi,E , , Manar,Y , and Rassias,T M . "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 M. (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
CHICAGO
E Elqorachi, Y Manar and T 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
VANCOUVER
Elqorachi E, Manar Y, Rassias T M. stability of the quadratic functional equation. IJNAA. 2010;1(2):26-35. doi: 10.22075/ijnaa.2010.72
International Journal of Nonlinear Analysis and Applications