Nearly quadratic \(n\)-derivations on non-Archimedean Banach algebras
Summary: Let \(n > 1\) be an integer, let \(A\) be an algebra, and \(X\) be an \(A\)-module. A quadratic function \(D : A \rightarrow X\) is called a quadratic \(n\)-derivation if \(D(\prod^n_{i=1} a_i) = D(a_1) a^2_2 \cdots a^2_n + a^2_1 D(a_2) a^2_3 \cdots a^2_n + \cdots + a^2_1 a^2_2 \cdots a^2_{n-1} D(a_n)\) for all \(a_1, \dots, a_n \in A\). We investigate the Hyers-Ulam stability of quadratic \(n\)-derivations from non-Archimedean Banach algebras into non-Archimedean Banach modules by using the Banach fixed point theorem.
scientific article; zbMATH DE number 6065462
scientific article