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Additive-quartic functional equation in non-Archimedean orthogonality spaces

김선우|이동환|강승연|이현주|손범준
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2012.03|한국수학논문집 (Korean Journal of Mathematics)|제20권 제1호|pp. 33-46

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참고문헌

키워드

Hyers-Ulam stabilitynon-Archimedean normed spaceorthogonally additive-quartic functional equationorthogonality space.
주제분류수학

초록

Using the direct method, we prove the Hyers-Ulam stability of the orthogonally additive-quartic functional equation \begin{align}f(2x+y)+ f(2x-y)&=4 f(x+y)+ 4 f(x-y) \nonumber \\ & + 10 f(x) + 14f(-x) - 3 f(y)-3f(-y)\end{align}for all $x, y$ with $x\perp y$, in non-Archimedean Banach spaces. Here $\perp$ is the orthogonality in the sense of R\"atz.

Abstract

Using the direct method, we prove the Hyers-Ulam stability of the orthogonally additive-quartic functional equation \begin{align}f(2x+y)+ f(2x-y)&=4 f(x+y)+ 4 f(x-y) \nonumber \\ & + 10 f(x) + 14f(-x) - 3 f(y)-3f(-y)\end{align}for all $x, y$ with $x\perp y$, in non-Archimedean Banach spaces. Here $\perp$ is the orthogonality in the sense of R\"atz.

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