Approximate Orthogonally Higher Ring Derivations

In this paper, we prove that every orthogonally higher ring derivation is a higher ring derivation. Also we find the general solution of the pexider or- thogonally higher ring derivations ( fn(x + y) = gn(x) + hn(y), x,y = 0, fn(xy) = P i+j=n gi (x)hj (y). Then we prove that for any approximate pexider orthogonally higher ring derivation under some control functions φ(x,y) and ψ(x,y), there exists a unique higher ring derivation D = {dn} ∞ n=0, near {fn} ∞ n=0, {gn} ∞ n=0 and {hn} ∞ n=0 estimated by φ and ψ.