Stability of a Quartic Functional Equation

Abstract EN

We obtain the general solution of the generalized quartic functional equation f ( x + m y ) + f ( x - m y ) = 2 ( 7 m - 9 ) ( m - 1 ) f ( x ) + 2 m 2 ( m 2 - 1 ) f ( y ) - ( m - 1 ) 2 f ( 2 x ) + m 2 { f ( x + y ) + f ( x - y ) } for a fixed positive integer m .

We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces.

We also investigate the Hyers-Ulam stability for the mentioned quartic functional equation in non-Archimedean spaces.