ORTHOGONAL STABILITY OF A CUBIC-QUARTIC FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN SPACES

Abstract

Using the fixed point method, we prove the Hyers-Ulam stability of the orthogonally cubic-quartic functional equation f (2x + y) + f (2x - y) = 3f (x + y) + f (-x - y) + 3 f (x - y) + f (y - x) +18f (x) + 6f (-x) -3f (y) - 3f (-y) (0.1) for all x, y with x perpendicular to y in non-Archimedean Banach spaces, where perpendicular to is the orthogonality in the sense of Ratz.