Approximate Orthogonally Higher Ring Derivations

	Approximate Orthogonally Higher Ring Derivations
Control and Optimization in Applied Mathematics
دوره 7، شماره 1، فروردین 2022، صفحه 93-106 اصل مقاله (390.97 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.30473/coam.2021.58866.1161
نویسنده
Sayed Kahlil Ekrami^*
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran
چکیده
In this paper‎, ‎we prove that every orthogonally higher ring derivation is a higher ring derivation‎. ‎Also we find the general solution of the pexider orthogonally higher ring derivations‎ ‎\begin{align}‎ ‎\left\{‎ ‎\begin{array}{lr}‎ ‎f_n(x+y)=g_n(x)+h_n(y)‎, ‎\;\left\langle x,y \right\rangle =0,\\‎ ‎f_n(xy) = \sum_{i+j=n} g_i(x)h_j(y)‎. ‎\end{array}‎ ‎\right‎. ‎\end{align}‎ ‎Then we prove that for any approximate pexider orthogonally higher ring derivation under some control functions $ \varphi(x,y) $ and $ \psi(x,y) $‎, ‎there exists a unique higher ring derivation $ D=\{d_n\}_{n=0}^\infty $‎, ‎near $ \{f_n\}_{n=0}^\infty $‎, ‎$ \{g_n\}_{n=0}^\infty $ and $ \{h_n\}_{n=0}^\infty $ estimated by $ \varphi $ and $ \psi $.
کلیدواژه‌ها
Approximation‎؛ ‎Control function‎؛ ‎Estimation‎؛ ‎Higher derivation

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