Let G be an abelian group, A a C∗-algebra and M a pre-Hilbert A-module with an A-valued
inner product⟨.,.⟩. We show if a function f: G→ M satisfies the inequality⟨ f (x)+ f (y), f (x)+ f …

This article presents the general solution f: G→ V of the following functional equation: f (x)− 4
f (x+ y)+ 6 f (x+ 2 y)− 4 f (x+ 3 y)+ f (x+ 4 y)= 0, x, y∈ G, where (G,+) is an abelian group and …

Asymptotic behavior of a generalized functional equation Page 1 http://www.aimspress.com/journal/Math
AIMS Mathematics, 7(4): 7001–7011. DOI: 10.3934/math.2022389 Received: 02 December …

Let $(G,+) $ be an abelian group and $ Y $ a linear space over the field $\Bbb {F}\in\{\Bbb
{R},\Bbb {C}\} $. In this paper, we investigate the conditional Cauchy functional equation\[f …

In this paper, we deal with a 2-linear functional equation. The Hyers-Ulam stability of this
functional equation is shown on some restricted unbounded domains, and the obtained …