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

摘要

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×Xn→A is an n-sesquilinear-quadratic mapping when h(rx,y;z1,…,zn)=h(x,ry;z1,…,zn)=h(x,y;rz1,z2,…,zn)=⋯=h(x,y;z1,z2,…,rzn)=rh(x,y;z1,z2,…,zn)(r>0,r≠1) holds for all x,y,z1,…,zn∈X.Moreover, we prove the generalized Hyers–Ulam–Rassias stability of an n-sesquilinear-quadratic mapping on a left Banach module over a unital C*-algebra.