{"paper":{"title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Marcelina Mocanu","submitted_at":"2024-12-29T19:53:34Z","abstract_excerpt":"We study in the setting of a metric space $\\left( X,d\\right) $ some generalizations of four hyperbolic-type metrics defined on open sets $G$ with nonempty boundary in the $n-$dimensional Euclidean space, namely Gehring-Osgood metric, Dovgoshey- Hariri-Vuorinen metric, Nikolov-Andreev metric and Ibragimov metric. In the definitions of these generalizations, the boundary $\\partial G$ of $G$ and the distance from a point $x$ of $G$ to $\\partial G$ are replaced by a nonempty proper closed subset $M$ of $X$ and by a $1-$Lipschitz function positive on $X\\setminus M$, respectively. For each generaliz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.20560","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.20560/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}