Stability of ternary antiderivation in ternary Banach algebras via fixed point theorem
In this paper, we introduce the concept of ternary antiderivation on ternary Banach algebras and investigate the stability of ternary antiderivation in ternary Banach algebras, associated to the $(\alpha,\beta)$-functional inequality: \begin{align*} &\Vert \mathcal{F}(x+y+z)-\mathcal{F}(x+z)-\...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Universidad de La Frontera
2023-08-01
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| Series: | Cubo |
| Subjects: | |
| Online Access: | https://cubo.ufro.cl/ojs/index.php/cubo/article/view/3451/2303 |
| Summary: | In this paper, we introduce the concept of ternary antiderivation on ternary Banach algebras and investigate the stability of ternary antiderivation in ternary Banach algebras, associated to the $(\alpha,\beta)$-functional inequality:
\begin{align*}
&\Vert \mathcal{F}(x+y+z)-\mathcal{F}(x+z)-\mathcal{F}(y-x+z)-\mathcal{F}(x-z)\Vert \nonumber\\
&\leq \Vert \alpha (\mathcal{F}(x+y-z)+\mathcal{F}(x-z)-\mathcal{F}(y))\Vert + \Vert \beta (\mathcal{F}(x-z)\\
&+\mathcal{F}(x)-\mathcal{F}(z))\Vert
\end{align*}
where $\alpha$ and $\beta$ are fixed nonzero complex numbers with $\vert\alpha \vert +\vert \beta \vert<2$ by using the fixed point method. |
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| ISSN: | 0716-7776 0719-0646 |