(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Mirzavaziri and Moslehian [13] introduced the concept of f-derivations and Sripattanet et al. [18] introduced a quadratic hom-der in Banach algebras. In this paper, we solve the system of quadratic functional equations align* { arrayc f(x+y)+f(x-y)=g(x)+ g(y), g(x+y2) + g(x-y2)= f(x) + f(y) array . 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.