Abstract:

Let A be a Banach algebra and M be a Banach A-module. An n-linear mapping f: An→M from An into M is called an n-cocycle if it satisfies that x1f(x1,…,xn+1)+(-1)n+1f(x1,…,xn)xn+1+∑ni=1(-1)if(x1,…,xi-1,xixi+1,xi+2,…,xn+1)=0 for all x1,…,xn+1∈A.It is proved that the n-cocycles from An into M are Hyers-Ulam stable.

Key words:  Banach algebra; n-cocycle; Hyers-Ulam stability