Approximately Vanishing of Topological Cohomology Groups
Abstract
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 n-th cohomology group approximately vanishes.
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