{"paper":{"title":"Best proximity pair results for relatively nonexpansive mappings in geodesic spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Adriana Nicolae, Aurora Fernandez Leon","submitted_at":"2013-06-03T11:22:20Z","abstract_excerpt":"Given $A$ and $B$ two nonempty subsets in a metric space, a mapping $T : A \\cup B \\rightarrow A \\cup B$ is relatively nonexpansive if $d(Tx,Ty) \\leq d(x,y) \\text{for every} x\\in A, y\\in B.$ A best proximity point for such a mapping is a point $x \\in A \\cup B$ such that $d(x,Tx)=\\text{dist}(A,B)$. In this work, we extend the results given in [A.A. Eldred, W.A. Kirk, P. Veeramani, Proximal normal structure and relatively nonexpansive mappings, Studia Math., 171 (2005), 283-293] for relatively nonexpansive mappings in Banach spaces to more general metric spaces. Namely, we give existence results "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0358","kind":"arxiv","version":2},"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"}