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An additive $(u, \beta)$-functional equation and linear mappings in Banach modules | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 140، دوره 13، شماره 2، مهر 2022، صفحه 1747-1755 اصل مقاله (410.69 K) | ||
| نوع مقاله: Special issue editorial | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.22580.2386 | ||
| نویسندگان | ||
| Siriluk Paokanta1؛ Choonkil Park2؛ Jung Rye Lee* 3 | ||
| 1Department of Mathematics, Hanyang University, Seoul 04763, Korea | ||
| 2Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea | ||
| 3Department of Data Science, Daejin University, Kyunggi 11159, Korea | ||
| تاریخ دریافت: 17 بهمن 1399، تاریخ بازنگری: 26 بهمن 1399، تاریخ پذیرش: 23 اسفند 1399 | ||
| چکیده | ||
| Let $A$ be a unital $C^*$-algebra. In this paper, we investigate the additive $(u, \beta)$-functional equation \begin{eqnarray}\label{0.1} f(x)+ u^* f(u y)+ f( z) = \beta^{-1} f(\beta(x+y+z)) \end{eqnarray} for all unitary elements $u$ in $A$ and for a fixed nonzero complex number $\beta$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive $(u, \beta)$-functional equation (\ref{0.1}) in Banach modules. | ||
| کلیدواژه‌ها | ||
| Hyers-Ulam stability؛ additive $(u, beta)$-functional equation؛ $A$-linear mapping؛ fixed point method؛ direct method؛ Banach module | ||
| مراجع | ||
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