Fixed points and generalized Hyers-Ulam stability of quadratic functional equations

摘要

Let X, Y be complex vector spaces. It is shown that if a mapping f : X → Y satisfies f (x + iy)+f (x . iy)=2f (x) . 2f (y) (0.1) or f (x + iy) . f (ix + y)=2f (x) . 2f (y) (0.2) for all x, y ∈ X , then the mapping f : X → Y satisfies f (x + y)+f (x . y)=2f (x)+ 2f (y) for all x, y ∈ X . Furthermore, we prove the generalized Hyers-Ulam stability of the functional equations (0.1) and (0.2) in complex Banach spaces