id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5719	Park, Choonkil; Donganont, Siriluk; Min, Se Won	Quadratic $f$-hom-ders in Banach Algebra Related to System of Quadratic Functional Equations	2025	10	.pdf	application/pdf	3437	217	80	and ∥f(x+ y) + f(x− y)− g(x)− g(y)∥ ≤ θ(∥x∥p + ∥y∥p), ∥g (x+y 2 ) + g (x−y 2 ) − f(x)− f(y)∥ ≤ θ(∥x∥p + ∥y∥p) for all x, y ∈ B. Then there exist unique quadratic mappings F,G : B → B such that ∥F (x)− f(x)∥ ≤ 2p + 2 2p − 4 θ∥x∥p, ∥G(x)− g(x)∥ ≤ 2(2p + 2) 2p − 4 θ∥x∥p for all x ∈ B. Proof. − f(x)− f(y)∥ ≤ θ(∥x∥p + ∥y∥q) and ∥g(xy)− f(x)g(y)− g(x)f(y)∥ ≤ θ(∥x∥p + ∥y∥q) for all x, y ∈ B. Then there exist unique quadratic mappings F,G : B → B such that G is a quadratic F -hom-der and ∥F (x)− f(x)∥ ≤ 2p + 2 2p − 4 θ∥x∥p, ∥G(x)− g(x)∥ ≤ 2(2p + 2) 2p − 4 θ∥x∥p for all x ∈ B. Proof.	cache/ejpam-5719.pdf	txt/ejpam-5719.txt