Finite Field Tarski-Maligranda Inequalities
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910184656338944 |
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| author | Krishna, K. Mahesh |
| author_facet | Krishna, K. Mahesh |
| contents | Let $\mathbb{F}$ be a sub-modulus field such that $2 \neq 0$. Let $\mathcal{X}$ be a sub-normed linear space over $\mathbb{F}$. Then we show that \begin{align*} \bigg|\|x\|-\|y\|\bigg|\leq \frac{2}{|2|}\|x+y\|+\frac{2}{|2|}\max\{\|x-y\|, \|y-x\|\}-(\|x\|+\|y\|) \end{align*} and \begin{align*} \bigg|\|x\|-\|y\|\bigg|\leq \|x\|+\|y\|-\frac{2}{|2|}\|x+y\|+\frac{2}{|2|}\max\{\|y-x\|, \|x-y\|\}. \end{align*} Above inequalities are finite field versions of important Tarski-Maligranda inequalities obained by Maligranda [\textit{Banach J. Math. Anal., 2008}]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_14194 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finite Field Tarski-Maligranda Inequalities Krishna, K. Mahesh General Mathematics 12E20, 46B20 Let $\mathbb{F}$ be a sub-modulus field such that $2 \neq 0$. Let $\mathcal{X}$ be a sub-normed linear space over $\mathbb{F}$. Then we show that \begin{align*} \bigg|\|x\|-\|y\|\bigg|\leq \frac{2}{|2|}\|x+y\|+\frac{2}{|2|}\max\{\|x-y\|, \|y-x\|\}-(\|x\|+\|y\|) \end{align*} and \begin{align*} \bigg|\|x\|-\|y\|\bigg|\leq \|x\|+\|y\|-\frac{2}{|2|}\|x+y\|+\frac{2}{|2|}\max\{\|y-x\|, \|x-y\|\}. \end{align*} Above inequalities are finite field versions of important Tarski-Maligranda inequalities obained by Maligranda [\textit{Banach J. Math. Anal., 2008}]. |
| title | Finite Field Tarski-Maligranda Inequalities |
| topic | General Mathematics 12E20, 46B20 |
| url | https://arxiv.org/abs/2604.14194 |