Orthogonal stability of an additive-quartic functional equation with the fixed point alternative

摘要

Using the fixed point method, we prove the Hyers-Ulam stability of the orthogonally additive-quartic functional equation f ( 2 x + y ) + f ( 2 x - y ) = 4 f ( x + y ) + 4 f ( x - y ) + 10 f ( x ) + 14 f ( - x ) - 3 f ( y ) - 3 f ( - y ) for all x, y with x ⊥ y, where ⊥ is the orthogonality in the sense of R?tz. AMS Subject Classification: Primary, 39B55; 47H10; 39B52; 46H25.