Automorphisms and derivations on the center of a ring

Let R be a ring, $sigma_{1}$ an automorphism of R and $delta_{1}$ a $sigma_{1}$-derivation of R. Let $sigma_{2}$ be an automorphism of $O_{1}(R) = R[x; sigma_{1}, delta_{1}]$, and $delta_{2}$ be a $sigma_{2}$-derivation of $O_{1}(R)$. Let $Ssubseteq Z(O_{1}(R))$,the center of $O_{1}(R)$. Then it is proved that $sigma_{i}$ is identity when restricted to $S$, and $delta_{i}$ is zero when restricted to $S$; $i = 1, 2$. The result is proved for iterated extensions also.