stability of the quadratic functional equation | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 4، دوره 1، شماره 2، 2010، صفحه 26-35 اصل مقاله (207.03 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2010.72 | ||
| نویسندگان | ||
| E. Elqorachi* 1؛ Y. Manar1؛ Th. M. Rassias2 | ||
| 1Department of Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir, Morocco | ||
| 2Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Hyers-Ulam-Rassias stability؛ quadratic functional equation | ||
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