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Stability of ternary antiderivation in ternary Banach algebras via fixed point theorem

Author
Dehghanian, Mehdi

Park, Choonkil

Sayyari, Yamin

Full text
https://cubo.ufro.cl/ojs/index.php/cubo/article/view/3451
10.56754/0719-0646.2502.273
Abstract
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{cases} &\| \mathcal{F}(x+y+z) - \mathcal{F}(x+z) - \mathcal{F}(y-x+z) - \mathcal{F}(x-z) \| \\ &\leq \| \alpha (\mathcal{F}(x+y-z) + \mathcal{F}(x-z) - \mathcal{F}(y)) \| + \| \beta (\mathcal{F}(x-z) \\ &+ \mathcal{F}(x) - \mathcal{F}(z)) \| \end{cases}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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Artes, Arquitectura y UrbanismoCiencias Agrarias, Forestales y VeterinariasCiencias Exactas y NaturalesCiencias SocialesDerechoEconomía y AdministraciónFilosofía y HumanidadesIngenieríaMedicinaMultidisciplinarias
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Universidad de ChileUniversidad Católica de ChileUniversidad de Santiago de ChileUniversidad de ConcepciónUniversidad Austral de ChileUniversidad Católica de ValparaísoUniversidad del Bio BioUniversidad de ValparaísoUniversidad Católica del Nortemore

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