{"paper":{"title":"Existence and Approximations for Order-Preserving Nonexpansive Semigroups over $\\rm{CAT}(\\kappa)$ Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Parin Chaipunya","submitted_at":"2018-11-28T14:16:04Z","abstract_excerpt":"In this paper, we discuss the fixed point property for an infinite family of order-preserving mappings which satisfy the Lipschitzian condition on comparable pairs. The underlying framework of our main results is a metric space of any global upper curvature bound $\\kappa \\in \\mathbb{R}$, i.e., a $\\rm{CAT}(\\kappa)$ space. In particular, we prove the existence of a fixed point for a nonexpasive semigroup on comparable pairs. Then, we propose and analyze two algorithms to approximate such a fixed point."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11585","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"}