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 |
| _version_ | 1797676880975888384 |
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| author | Mehdi Dehghanian Choonkil Park Yamin Sayyari |
| author_facet | Mehdi Dehghanian Choonkil Park Yamin Sayyari |
| author_sort | Mehdi Dehghanian |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T22:35:53Z |
| format | Article |
| id | doaj.art-61a02a848ad64ed6bf16f4e9454a0c9d |
| institution | Directory Open Access Journal |
| issn | 0716-7776 0719-0646 |
| language | English |
| last_indexed | 2024-03-11T22:35:53Z |
| publishDate | 2023-08-01 |
| publisher | Universidad de La Frontera |
| record_format | Article |
| series | Cubo |
| spelling | doaj.art-61a02a848ad64ed6bf16f4e9454a0c9d2023-09-22T13:47:46ZengUniversidad de La FronteraCubo0716-77760719-06462023-08-0125227328810.56754/0719-0646.2502.273Stability of ternary antiderivation in ternary Banach algebras via fixed point theoremMehdi Dehghanian0https://orcid.org/0000-0002-5348-1333Choonkil Park1https://orcid.org/0000-0001-6329-8228Yamin Sayyari2https://orcid.org/0000-0001-8019-3655Department of Mathematics, Sirjan University of Technology, Sirjan, Iran.Research Institute for Convergence of Basic Science, Hanyang University, Seoul 04763, South Korea.Department of Mathematics, Sirjan University of Technology, Sirjan, Iran.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.https://cubo.ufro.cl/ojs/index.php/cubo/article/view/3451/2303hyers-ulam stabilitystabilityfixed point methodternary antiderivationternary banach algebraadditive functional inequality |
| spellingShingle | Mehdi Dehghanian Choonkil Park Yamin Sayyari Stability of ternary antiderivation in ternary Banach algebras via fixed point theorem Cubo hyers-ulam stability stability fixed point method ternary antiderivation ternary banach algebra additive functional inequality |
| title | Stability of ternary antiderivation in ternary Banach algebras via fixed point theorem |
| title_full | Stability of ternary antiderivation in ternary Banach algebras via fixed point theorem |
| title_fullStr | Stability of ternary antiderivation in ternary Banach algebras via fixed point theorem |
| title_full_unstemmed | Stability of ternary antiderivation in ternary Banach algebras via fixed point theorem |
| title_short | Stability of ternary antiderivation in ternary Banach algebras via fixed point theorem |
| title_sort | stability of ternary antiderivation in ternary banach algebras via fixed point theorem |
| topic | hyers-ulam stability stability fixed point method ternary antiderivation ternary banach algebra additive functional inequality |
| url | https://cubo.ufro.cl/ojs/index.php/cubo/article/view/3451/2303 |
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