Let be an algebra, and let , be ring automorphisms of . An additive mapping is called a -derivation if for all . Moreover, an additive mapping is said to be a generalized -derivation if there exists a -derivation such that for all . In this paper, we investigate the superstability of generalized -derivations in non-Archimedean algebras by using a version of fixed point theorem via Cauchy’s functional equation.
M. Eshaghi Gordji. M. B. Ghaemi. G. H. Kim. Badrkhan Alizadeh. "Stability and Superstability of Generalized (, )-Derivations in Non-Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation." J. Appl. Math. 2011 1 - 11, 2011. https://doi.org/10.1155/2011/726020