Bulletin of the
Korean Mathematical Society BKMS

In this paper, using the Baire category theorem we investigate the Hyers-Ulam stability problem of pexiderized Jensen functional equation \begin{equation} 2f \left(\frac{x+y}{2} \right) - g(x) - h(y) = 0 \nonumber \end{equation} and pexiderized Jensen type functional equations \begin{align} & f(x+y)+g(x-y)-2h(x)=0, \nonumber \\ & f(x+y)-g(x-y)-2h(y)=0 \nonumber \end{align} on a set of Lebesgue measure zero. As a consequence, we obtain asymptotic behaviors of the functional equations.

Keywords: Baire category theorem, first caetgory, second category, Hyers-Ulam stability, pexiderized Jensen functional equation, pexiderized Jensen type functional equation, restricted domain

MSC numbers: 39B82