{"paper":{"title":"Characterization of a generalized triangle inequality in normed spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"F. Dadipour, J.M. Rassias, M.S. Moslehian, S.-E. Takahasi","submitted_at":"2011-09-08T17:07:28Z","abstract_excerpt":"For a normed linear space $(X,|\\cdot|)$ and $p>0$ we characterize all $n$-tuples $(\\mu_1,...,\\mu_n)\\in\\mathbb{R}^{n}$ for which the generalized triangle inequality of the second type $$\\|x_1+...+x_n\\|^p\\leq\\frac{|x_1|^p}{\\mu_1}+...+\\frac{|x_n|^p}{\\mu_n}$$ holds for any $x_1,...,x_n\\in X$. We also characterize $(\\mu_1,...,\\mu_n)\\in\\mathbb{R}^{n}$ for which the reverse of the inequality above holds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1773","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}