ADDITIVE-QUARTIC FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN ORTHOGONALITY SPACES

Abstract

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