Orthogonal Stability of an Additive-quartic Functional Equation in Non-Archimedean Spaces

Abstract

Using fixed point 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)\nonumber \end{align} for all $x, y$ with $x\perp y$, in non-Archimedean Banach spaces. Here $\perp$ is the orthogonality in the sense of Ratz.