Non-Archimedean Tarski-Maligranda Inequalities
Functional Analysis
2026-05-12 v2 Number Theory
Abstract
In 1930, Tarski observed that \begin{align*} \bigg||r|-|s|\bigg|=|r-s|+ |r+s|-(|r|+|s|), \quad \forall r, s \in \mathbb{R}. \end{align*} In 2008, Maligranda converted the previous equality into inequalities that are valid in every normed linear space. We derive non-Archimedean versions of Tarski-Maligranda inequalities. Difference between Archimedean and non-Archimedean inequalities is surprising.
Cite
@article{arxiv.2603.01446,
title = {Non-Archimedean Tarski-Maligranda Inequalities},
author = {K. Mahesh Krishna},
journal= {arXiv preprint arXiv:2603.01446},
year = {2026}
}
Comments
Statement of Theorem 2.1 corrected; Example 2.2 and Example 2.3 are new. 4 Pages, 0 Figures