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

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{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.