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.