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

Mehdi Dehghanian; Choonkil Park; Yamin Sayyari

doi:10.56754/0719-0646.2502.273

DOI:

https://doi.org/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.

Keywords

Hyers-Ulam stability , stability , fixed point method , ternary antiderivation , ternary Banach algebra , additive functional inequality

Mathematics Subject Classification:

47B47 , 11E20 , 17B40 , 39B72 , 47H10

Mehdi Dehghanian Department of Mathematics, Sirjan University of Technology, Sirjan, Iran. https://orcid.org/0000-0002-5348-1333
Choonkil Park Research Institute for Convergence of Basic Science, Hanyang University, Seoul 04763, South Korea. https://orcid.org/0000-0001-6329-8228
Yamin Sayyari Department of Mathematics, Sirjan University of Technology, Sirjan, Iran. https://orcid.org/0000-0001-8019-3655

Pages: 273–288
Date Published: 2023-08-08
Vol. 25 No. 2 (2023)

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