On additive functions with additional derivation properties
Classical Analysis and ODEs
2020-06-22 v1
Abstract
The purpose of this paper is to introduce the notion of a generalized derivation which derivates a prescribed family of smooth vector-valued functions of several variables. The basic calculus rules are established and then a result derived which shows that if a function satisfies an addition theorem whose determining operation is derivable with respect to an additive function , then the function is itself derivable with respect to . As an application of this approach, new proof of a generalization of a recent result of Maksa is obtained. We also extend the result of Nishiyama and Horinouchi and formulate two open problems.
Cite
@article{arxiv.2006.11028,
title = {On additive functions with additional derivation properties},
author = {Richárd Grünwald and Zsolt Páles},
journal= {arXiv preprint arXiv:2006.11028},
year = {2020}
}