Let be an algebra and . A sequence of mappings on is called a higher ring derivation of rank if for each ,
It is obvious that is a homomorphism and is a -derivation in the sense of M. Mirzavaziri and M. S. Moslehian [Proc. Am. Math. Soc. 134, No. 11, 3319–3327 (2006; Zbl 1116.46061)]. In this paper the authors use ideas of R. Badora [J. Math. Anal. Appl. 276, No. 2, 589–597 (2002; Zbl 1014.39020)] and T. Miura, G. Hirasawa and S.-E. Takahasi [J. Math. Anal. Appl. 319, No. 2, 522–530 (2006; Zbl 1104.39025)] to establish the stability of higher derivations on Banach algebras as well as superstability of such mappings under the surjectivity of .