Cauchy--Schwarz-type inequalities for additive functions
Rings and Algebras
2024-02-14 v1
Abstract
The main goal of this paper is to show that if a real valued function defined on a groupoid satisfies a certain Levi--Civita-type functional equation, then it also fulfills a Cauchy--Schwarz-type functional inequality. In particular, if the groupoid is the multiplicative structure of commutative ring, then we can establish the existence of nontrivial additive functions satisfying inequalities connected to the multiplicative structure.
Cite
@article{arxiv.2402.08587,
title = {Cauchy--Schwarz-type inequalities for additive functions},
author = {Zsolt Páles and Mahmood Kamil Shihab},
journal= {arXiv preprint arXiv:2402.08587},
year = {2024}
}