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Hyers-Ulam stability of a quadratic-additive functional equation in non-Archimedean fuzzy $\varphi$-2-normed spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 1، دوره 16، شماره 4، تیر 2025، صفحه 1-13 اصل مقاله (457.52 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.28228.3838 | ||
| نویسندگان | ||
| Kandhasamy Tamilvanan1؛ Jung Rye Lee* 2؛ Choonkil Park3 | ||
| 1Department of Mathematics, Government Arts College for Men, Krishnagiri- 635 001, Tamil Nadu, India | ||
| 2Department of Data Science, Daejin University, Kyunggi 11159, Korea | ||
| 3Research Institute for Convergence of Basic Science, Hanyang University, Seoul 04763, Korea | ||
| تاریخ دریافت: 10 مرداد 1401، تاریخ پذیرش: 11 شهریور 1401 | ||
| چکیده | ||
| In this work, we introduce the following quadratic-additive functional equation \begin{align*} &\psi\left(\sum_{a=1}^{n} v_{a}\right)+\sum_{a=1}^{n}\psi\left(-v_{a}+\sum_{b=1;a\neq b}^{n} v_{b}\right)\nonumber \\= &\left(n-3\right) \sum_{1\leq a<b\leq n}\psi\left( v_{a}+ v_{b}\right)-\left(n^{2}-5n+2\right)\sum_{a=1}^{n} \left[ \frac{\psi(v_{a})+\phi(-v_{a})}{2}\right] -\left(n^{2}-5n+4\right)\sum_{a=1}^{n} \left[\frac{\psi(v_{a})-\phi(-v_{a})}{2}\right] \end{align*} where $n$ is a nonnegative integer in $\mathbb{N}-\{0,1,2\}$, and we prove the Hyers-Ulam stability of the quadratic-additive functional equation in non-Archimedean fuzzy $\varphi$-2-normed space by utilizing two different techniques. | ||
| کلیدواژهها | ||
| Hyers-Ulam stability؛ non-Archimedean $\varphi$-2-normed space؛ quadratic-additive functional equation؛ fixed point method | ||
| مراجع | ||
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