Orthogonal stability of an additive-quadratic functional equation in non-archimedean spaces (Q2917644)

By applying some ideas from \textit{R. Ger} and \textit{J. Sikorska} [Bull. Polish Acad. Sci. Math. 43, 143--151 (1995; Zbl 0833.39007)] the authors establish the Hyers-Ulam stability of the orthogonally additive-quadratic functional equation NEWLINE\[NEWLINE2f(\frac{x+y}{2})+2f(\frac{x-y}{2})=\frac{3}{2}f(x)-\frac{1}{2}f(-x)+\frac{1}{2}f(y)+\frac{1}{2}f(-y)NEWLINE\]NEWLINE for each \(x, y\in X\) with \(x \perp y\), in non-Archimedian Banach spaces, for odd and even mappings. Recall that the orthogonality ``\(\perp\)'' is in the sense of \textit{J. Rätz} [Abh. Math. Semin. Univ. Hamb. 59, 23--33 (1989; Zbl 0712.39023)].