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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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참고문헌 (32)
참고문헌 신청
A. Bahyrycz / 2013 / On solutions of the d'Alembert equation on a restricted domain / Aequationes Math 85(1-2):169~183
B. Batko / 2008 / Stability of an alternative functional equation / J. Math. Anal. Appl 339(1):303~311
J. Brzdek / 2009 / On a method of proving the Hyers-Ulam stability of functional equations on restricted domains / Aust. J. Math. Anal. Appl 6(1):10
J. Brzdek / 2009 / On the quotient stability of a family of functional equations / Nonlinear Anal 71(10):4396~4404
J. Brzdek / 2015 / Recent developments of the conditional stability of the homomorphism equation / Banach J. Math. Anal 9(3):278~326
B. Batko / 2008 / Stability of an alternative functional equation / J. Math. Anal. Appl 339(1):303~311
J. Brzdek / 2009 / On a method of proving the Hyers-Ulam stability of functional equations on restricted domains / Aust. J. Math. Anal. Appl 6(1):10
J. Brzdek / 2009 / On the quotient stability of a family of functional equations / Nonlinear Anal 71(10):4396~4404
J. Brzdek / 2015 / Recent developments of the conditional stability of the homomorphism equation / Banach J. Math. Anal 9(3):278~326
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