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Asymptotic behavior of generalized quadratic mappings | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 92، دوره 12، شماره 1، مرداد 2021، صفحه 1153-1165 اصل مقاله (387.69 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.4982 | ||
| نویسندگان | ||
| Hark Mahn Kim1؛ Ick-Soon Chang* 2 | ||
| 1Department of Mathematics, Chungnam National University 99 Daehangno, Yuseong-gu, Daejeon 305-764, Korea | ||
| 2Department of Mathematics, Chungnam National University, 99 Daehangno, Yuseong-gu, Daejeon 34134, Korea | ||
| تاریخ دریافت: 21 بهمن 1399، تاریخ بازنگری: 15 اسفند 1399، تاریخ پذیرش: 23 اسفند 1399 | ||
| چکیده | ||
| We show in this paper that a mapping $f$ satisfies the following functional equation \begin{eqnarray*} \biguplus_{x_2,\cdots,x_{d+1}}^{d}f(x_1) = 2^{d} \sum_{i=1}^{d+1}f(x_i), \end{eqnarray*} if and only if it is quadratic. In addition, we investigate generalized Hyers-Ulam stability problem for the equation, and thus obtain an asymptotic property of quadratic mappings as applications. | ||
| کلیدواژه‌ها | ||
| Stability؛ Parallel polyhedron equality؛ Generalized quadratic mappings | ||
| مراجع | ||
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