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Let $f: \mathbb R^3 \to \mathbb R $. In this paper we prove the stability of functional inequalities \begin{align} |f(ux+vy, uy-vx,zw)-f(x, y,z)f(u,v,w)|&\le\phi(u, v, w) \,\, {\rm or}\,\,\phi(x, y, z), \nonumber \\ |f(ux-vy, uy-vx,zw)-f(x, y,z)f(u,v,w)|&\le\phi(u, v, w) \,\,{\rm or}\,\,\phi(x, y, z) \nonumber \end{align} for all $x,y,z,u,v,w \in \mathbb R$. Furthermore, we give refined descriptions of bounded functions satisfying the inequalities as in Albert and Baker \cite{AB}.
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참고문헌 (9)
참고문헌 신청
M. Albert / 1982 / Bounded solutions of a functional inequality / Canad. Math. Bull 25(4):491~495
J. A. Baker / 1979 / The stability of the equation f(x + y) =f(x)f(y) / Proc. Amer. Math. Soc 74(2):242~246
J. Chung / 2015 / On an exponential functional inequality and its distributional version / Canad. Math. Bull 58(1):30~43
J. Chung / 2014 / On two functional equations originating from number theory / Proc. Indian Acad. Sci. Math. Sci 124(4):563~572
J. Chung / Stability of functional equations arising from number theory and determinant of matrices
J. A. Baker / 1979 / The stability of the equation f(x + y) =f(x)f(y) / Proc. Amer. Math. Soc 74(2):242~246
J. Chung / 2015 / On an exponential functional inequality and its distributional version / Canad. Math. Bull 58(1):30~43
J. Chung / 2014 / On two functional equations originating from number theory / Proc. Indian Acad. Sci. Math. Sci 124(4):563~572
J. Chung / Stability of functional equations arising from number theory and determinant of matrices
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