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

Existence and uniqueness of solutions to a first-order differential equation via fixed point theorem in orthogonal metric space

In this paper, among the other things, we show that the solution of the first-orderdifferential equation is a fixed point of an integral operator from an orthogonal metric space into itself. This approach provides a new proof of the classical existence and uniqueness theorems of solutions to a first-order differential equation