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January 23, 2026Open Access

Non-Archimedean Tarski-Maligranda Inequalities

Key Points

The aim is to derive non-Archimedean versions of the Tarski-Maligranda inequalities.
Reviewed Tarski's initial equality from 1930.
Explored Maligranda's inequalities from 2008 in normed linear spaces.
Developed non-Archimedean adaptations of these inequalities.
Successfully derived non-Archimedean inequalities.
Identified surprising differences between Archimedean and non-Archimedean forms.

Abstract

In 1930, Tarski observed that align* ||r|-|s||=|r-s|+ |r+s|- (|r|+|s|), r, s R. 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.

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Cite This Study

MAHESH KRISHNA K (Wed,) studied this question.

synapsesocial.com/papers/69730f18c8125b09b0d1eef4 https://doi.org/https://doi.org/10.5281/zenodo.18321374

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Non-Archimedean Tarski-Maligranda Inequalities | Synapse