Stability and superstability of generalized \((\theta, \phi)\)-derivations in non-Archimedean algebras: fixed point theorem via the additive Cauchy functional equation
Summary: Let \(A\) be an algebra, and let \(\theta, \phi\) be ring automorphisms of \(A\). An additive mapping \(H : A \rightarrow A\) is called a \((\theta, \phi)\)-derivation if \(H(xy) = H(x)\theta(y) + \phi(x)H(y)\) for all \(x, y \in A\). Moreover, an additive mapping \(F : A \rightarrow A\) is said to be a generalized \((\theta, \phi)\)-derivation if there exists a \((\theta, \phi)\)-derivation \(H : A \rightarrow A\) such that \(F(xy) = F(x)\theta(y) + \phi(x)H(y)\) for all \(x, y \in A\). In this paper, we investigate the superstability of generalized \((\theta, \phi)\)-derivations in non-Archimedean algebras by using a version of fixed point theorem via Cauchy's functional equation.
scientific article; zbMATH DE number 6021619
scientific article