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Stability of pexiderized Jensen and Jensen type functional equations on restricted domains

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대한수학회 (The Korean Mathematical Society)|2019.05|대한수학회보 (Bulletin of the KMS)|제56권 제3호|pp. 801-813|DOI 10.4134/BKMS.b180607

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키워드

Hyers-Ulam stabilityBaire category theoremfirst caetgorysecond categorypexiderized Jensen functional equationpexiderized Jensen type functional equationrestricted domain
주제분류수학

초록

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.

Abstract

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.

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