A trick for investigation of approximate derivations

We utilize the notion of module extension to reduce the problem of stability of derivations to that of ring homomorphisms studied by R. Badora in the context of Banach bimodules over Banach algebras

GENERALIZED HYERS–ULAM STABILITY OF AN AQCQ-FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN BANACH SPACES

Abstract. In this paper, we prove the generalized Hyers–Ulam stability of the following additive-quadratic-cubic-quartic functional equation f(x + 2y) + f(x − 2y) = 4f(x + y) + 4f(x − y) − 6f(x) + f(2y) + f(−2y) − 4f(y) − 4f(−y) in non-Archimedean Banach spaces. 1. Introduction an