Partial stabilities and partial derivations of \(n\)-variable functions (Q2653979)

The authors introduce the notion of the partial derivations of an \(n\)-variable function from a normed algebra \({\mathcal{A}}_1 \times {\mathcal{A}}_1 \times \cdots \times {\mathcal{A}}_n\) into a Banach algebra \({\mathcal{B}}\). Using this notion, they prove the Hyers-Ulam-Rassias stability for the partial derivations. Furthermore, some results about the applications of derivations such as the extended derivations and the approximately higher derivations are given in this paper.