Non-Archimedean Tarski-Maligranda Inequalities

TL;DR

This paper develops non-Archimedean analogues of Tarski-Maligranda inequalities, highlighting surprising differences from the classical Archimedean case in normed linear spaces.

Contribution

It introduces non-Archimedean versions of classical inequalities, expanding their applicability beyond traditional real number contexts.

Findings

Derived non-Archimedean inequalities analogous to Tarski-Maligranda inequalities.

Identified surprising differences between Archimedean and non-Archimedean inequalities.

Extended the scope of these inequalities to non-Archimedean settings.

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.