Let A be an algebra. A double centralizer of A is a pair (L,R) of linear mappings L,R:A→A such that L(ab)=L(a)b, R(ab) =aR(b), aL(b) =R(a)b(a,b∈A). We establish the generalized stability of double centralizers associated with the Cauchy, Jensen, and Trif functional equations in the framework of Banach algebras. Introducing a notion of approximate double centralizer we also investigate the superstability of double centralizers of Banach algebras strongly without order.

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