{"paper":{"title":"Best Proximity Point Theorems for Asymptotically Relatively Nonexpansive Mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"P. Veeramani, S. Rajesh","submitted_at":"2016-11-08T11:36:00Z","abstract_excerpt":"Let $(A, B)$ be a nonempty bounded closed convex proximal parallel pair in a nearly uniformly convex Banach space and $T: A\\cup B \\rightarrow A\\cup B$ be a continuous and asymptotically relatively nonexpansive map. We prove that there exists $x \\in A\\cup B$ such that $\\|x - Tx\\| = \\emph{dist}(A, B)$ whenever $T(A) \\subseteq B$, $T(B) \\subseteq A$. Also, we establish that if $T(A) \\subseteq A$ and $T(B) \\subseteq B$, then there exist $x \\in A$ and $y\\in B$ such that $Tx = x$, $Ty = y$ and $\\|x - y\\| = \\emph{dist}(A, B)$. We prove the aforesaid results when the pair $(A, B)$ has the rectangle pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02484","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"}