Generalized Hyers–Ulam–Rassias stability of n-sesquilinear-quadratic mappings on Banach modules over -algebras

Assume that X is a left Banach module over a unital C * -algebra A. It is shown that almost every n-sesquilinear-quadratic mapping h : X × X × X n → A is an n-sesquilinear-quadratic mapping when h ( rx , y ; z 1 , … , z n ) = h ( x , ry ; z 1 , … , z n ) = h ( x , y ; r z 1 , z 2 , … , z n ) = ⋯ = h ( x , y ; z 1 , z 2 , … , r z n ) = rh ( x , y ; z 1 , z 2 , … , z n ) ( r > 0 , r ≠ 1 ) holds for all x , y , z 1 , … , z n ∈ X . er, we prove the generalized Hyers–Ulam–Rassias stability of an n-sesquilinear-quadratic mapping on a left Banach module over a unital C * -algebra.