On the generalized Hyers–Ulam stability of multi-quadratic mappings

A mapping f:Vn⟶Wf:Vn⟶W, where VV is a commutative group, WW is a linear space, and n≥2n≥2 is an integer, is called multi-quadratic if it is quadratic in each variable. In this paper, we prove the generalized Hyers–Ulam stability of multi-quadratic mappings in Banach spaces and complete non-Archimedean spaces.