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 $n,H^n(A,X)=0$ if and only if the $n$-th cohomology group approximately vanishes.

18 pages, minor corrections

References in corpus (1)

• Approximate $(\sigma -\tau )$-Contractibility

Cited by in corpus (10)

• Approximate Homomorphisms of Ternary Semigroups
• Hyers-Ulam-Rassias Stability of Generalized Derivations
• Satbility of Ternary Homomorphisms via Generalized Jensen Equation
• Stability of Generalized Jensen Equation on Restricted Domains
• Superstability of adjointable mappings on Hilbert $C^{\ast }$-modules
• Vanishing of the first $(\sigma ,\tau )$-cohomology group of triangular Banach algebras
• $\theta$-derivations on $J{B}^{\ast }$-triples
• Stability of ternary Jordan homomorphisms and derivations associated to the generalized Jensen equation
• Nearly generalized Jordan derivations
• Approximate $C^{\ast }$-Ternary Ring Homomorphisms