Quadratic $f$-hom-ders in Banach Algebra Related to System of Quadratic Functional Equations (European Journal of Pure and Applied Mathematics, 2025)
Mirzavaziri and Moslehian [13] introduced the concept of f-derivations and Sripattanetet al. [18] introduced a quadratic hom-der in Banach algebras. In this paper, we solve the system of quadratic  functional equations\begin{align*}\left \{\begin{array}{c}f(x+y)+f(x-y)=g(x)+ g(y), \\g\left(\frac{x+y}{2}\right) + g\left(\frac{x-y}{2}\right)= f(x) + f(y)\end{array}\right.\end{align*}Using Mirzavaziri and Moslehian’s idea and Sripattanet et al.’s idea, we define a quadratic f-hom-der in Banach algebras, and we investigate the Hyers-Ulam stability of quadratic f-hom-ders in Banach algebras.