A Pexider difference associated to a Pexider quartic functional equation in topological vector spaces

Abstract

Let $\left(G,+\right)$ be an Abelian group and $X$ be a sequentially complete Hausdorff topological vector space over the field $\mathbb{Q}$ of rational numbers. We deal with a Pexider difference

$$2f\left(2x+y\right)+2f\left(2x-y\right)-2g\left(x+y\right)-2g\left(x-y\right)-12g\left(x\right)+3g\left(y\right),$$

where $f$ and $g$ are mappings defined on $G$ and taking values in $X$. We investigate the Hyers–Ulam stability of the Pexiderized quartic functional equation

$$2f\left(2x+y\right)+2f\left(2x-y\right)=2g\left(x+y\right)+2g\left(x-y\right)+12g\left(x\right)-3g\left(y\right)$$

in topological vector spaces.