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. M. (2010). stability of the quadratic functional equation. International Journal of Nonlinear Analysis and Applications, 1(2), 26–35. https://doi.org/10.22075/ijnaa.2010.72
MLA
Elqorachi, E., Manar, Y., & 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
Elqorachi, E., Manar, Y. & 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
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