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)=∑i=0nfi(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=0n=0 (respectively n=1n=1 and f0f0 is an identity operator).