Vol. 6, No. 4, 2013

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

Saeid Ostadbashi, Abbas Najati, Mahsa Solaimaninia and Themistocles M. Rassias

Vol. 6 (2013), No. 4, 505–510
Abstract

Let $\left(G,+\right)$ be an Abelian group and $X$ be a sequentially complete Hausdorff topological vector space over the field $ℚ$ 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.

Keywords
Hyers–Ulam stability, quartic mapping, topological vector space
Mathematical Subject Classification 2010
Primary: 39B82
Secondary: 34K20, 54A20