Approximate derivations of order $n$

TL;DR

This paper establishes characterization theorems for higher order derivations, demonstrating the stability of their defining systems and presenting additional theorems inspired by N. G. de Bruijn.

Contribution

It provides new characterization theorems and stability results for higher order derivations, expanding theoretical understanding in this area.

Findings

Proved stability of the system defining higher order derivations

Presented characterization theorems for higher order derivations

Extended results in the spirit of de Bruijn

Abstract

The aim of this paper is to prove characterization theorems for higher order derivations. Among others we prove that the system defining higher order derivations is stable. Further characterization theorems in the spirit of N.~G.~de Bruijn will also be presented.