{"paper":{"title":"Pazy's fixed point theorem with respect to the partial order in uniformly convex Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Rudong Chen, Yisheng Song","submitted_at":"2016-06-27T11:21:27Z","abstract_excerpt":"In this paper, the Pazy's Fixed Point Theorems of monotone $\\alpha-$nonexpansive mapping $T$ are proved in a uniformly convex Banach space $E$ with the partial order \"$\\leq$\". That is, we obtain that the fixed point set of $T$ with respect to the partial order \"$\\leq$\" is nonempty whenever the Picard iteration $\\{T^nx_0\\}$ is bounded for some initial point $x_0$ with $x_0\\leq Tx_0$ or $Tx_0\\leq x_0$. When restricting the demain of $T$ to the cone $P$, a monotone $\\alpha-$nonexpansive mapping $T$ has at least a fixed point if and only if the Picard iteration $\\{T^n0\\}$ is bounbed. Furthermore, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08216","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"}