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arXiv · 1109.1773

Characterization of a generalized triangle inequality in normed spaces

F. Dadipour·M. S. Moslehian·J. M. Rassias·S. -E. Takahasi
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Abstract

For a normed linear space $(X,|\cdot|)$ and $p>0$ we characterize all $n$-tuples $(μ_1,...,μ_n)\in\mathbb{R}^{n}$ for which the generalized triangle inequality of the second type $$\|x_1+...+x_n\|^p\leq\frac{|x_1|^p}{μ_1}+...+\frac{|x_n|^p}{μ_n}$$ holds for any $x_1,...,x_n\in X$. We also characterize $(μ_1,...,μ_n)\in\mathbb{R}^{n}$ for which the reverse of the inequality above holds.

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F. Dadipour, M. S. Moslehian, J. M. Rassias, S. -E. Takahasi. 2011-09-08. Characterization of a generalized triangle inequality in normed spaces. https://arxiv.org/abs/1109.1773

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