A Pexider system of additive functional equations in Banach algebras

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2024年2月23日

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Mehdi Dehghanian,
Yamin Sayyari,
Siriluk Donganont,
Choonkil Park

摘要

In this paper, we solve the system of functional equations ${\begin{matrix} f (x + y) + g (y - x) = 2 f (x), \\ g (x + y) - f (y - x) = 2 g (y) \end{matrix}$ $\begin{aligned} \textstyle\begin{cases} f(x+y)+g(y-x)=2f(x), \\ g(x+y)-f(y-x)=2g(y) \end{cases}\displaystyle \end{aligned}$ and we investigate the stability of g-derivations in Banach algebras.