Stability of pexider Jensen and Jensen type functional equations on restricted domains
Bull. Korean Math. Soc.
Published online 2019 Mar 13
Chang-Kwon Choi
Kunsan National University
Abstract : In this paper, using the Baire category theorem we investigate the Hyers-Ulam stability problem of
pexider Jensen functional equation
\begin{equation}
2f \left(\frac{x+y}{2} \right) - g(x) - h(y) = 0 \nonumber
\end{equation}
and pexider 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 : Hyers-Ulam stability, Jensen functional equation, Jensen type functional equation, pexider Jensen functional equation, pexider Jensen type functional equation, restricted domain
MSC numbers : 39B82
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