A fixed point approach to the stability of sextic Lie *-derivations

Abstract

We obtain a general solution of the sextic functional equation f (ax + by) + f (ax − by) + f (bx + ay) + f (bx − ay) = (ab) 2 (a 2 + b 2)[ f (x + y) + f (x − y)] + 2(a 2 − b 2)(a 4 − b 4)[ f (x) + f (y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.