Approximately vanishing of topological cohomology groups

In this paper, we establish the pexiderized stability of coboundaries and cocycles and use them to investigate the Hyers–Ulam stability of some functional equations. We prove that for each Banach algebra A, Banach A-bimodule X and positive integer n,Hn(A,X)=0 if and only if the nth cohomology group approximately vanishes.