On approximately higher ring derivations

In this paper, we examine the Hyers–Ulam, the Isac and Rassias-type stability and the Bourgin-type superstability of a functional inequality corresponding to the following functional equation, respectively: fn(xy) = n i=0 fi(x)fn−i(y). In particular, an additive operator satisfying the above equation is said to be a ring homomorphism (respectively a ring derivation) if n = 0 (respectively n = 1 and f0 is an identity operator). © 2008 Elsevier Inc. All rights reserved