Alienation of the Set-Valued Drygas-Additive and Quadratic-Additive Functional Equations

Abstract

Consider $Y$ as a real Hausdorff topological vector space and $(G,+)$ as a Abelian group uniquely divisible by 2. In this paper, the solutions and stability of the Pexiderized set-valued functional equations\begin{align*} f(x+y)+f(x-y)+g(x+y)&=2f(x)+f(y)+f(-y)+g(x)\\ & \quad +g(y), \\ f(x+y)+f(x-y)+g(x+y)&=2f(x)+2f(y)+g(x)+g(y),\end{align*}are investigated, where $f$ and $g$ are unknown functions from $G$ to $cc(Y)$.

Keywords

• set-valued function
• quadratic function
• drygas function
• hukuhara difference