{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:GV4PHCEDFR2LQAOOZ7LTNEZIPZ","short_pith_number":"pith:GV4PHCED","schema_version":"1.0","canonical_sha256":"3578f388832c74b801cecfd73693287e42033960254df478c6ef6883743d05eb","source":{"kind":"arxiv","id":"1606.08216","version":1},"attestation_state":"computed","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, "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1606.08216","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-27T11:21:27Z","cross_cats_sorted":[],"title_canon_sha256":"118b191281e89cdd7bd49a72899e54de37e07ff1916e7a089f2ad0a6d1168bf3","abstract_canon_sha256":"8b8e401996e09c396d91a39871b4f6627ecb00a4f6eb7ddda0918b31eaa1ea5a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:52.530726Z","signature_b64":"aA44JPgXPuHI/Zj0UX2UeT130U1e8FAaOF2Mpv9k6qOEhfnhvxFja74lBuWgTdZUbrZGm9AburrFHThYUCWdBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3578f388832c74b801cecfd73693287e42033960254df478c6ef6883743d05eb","last_reissued_at":"2026-05-18T01:11:52.530409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:52.530409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1606.08216","created_at":"2026-05-18T01:11:52.530460+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.08216v1","created_at":"2026-05-18T01:11:52.530460+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08216","created_at":"2026-05-18T01:11:52.530460+00:00"},{"alias_kind":"pith_short_12","alias_value":"GV4PHCEDFR2L","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"GV4PHCEDFR2LQAOO","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"GV4PHCED","created_at":"2026-05-18T12:30:19.053100+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GV4PHCEDFR2LQAOOZ7LTNEZIPZ","json":"https://pith.science/pith/GV4PHCEDFR2LQAOOZ7LTNEZIPZ.json","graph_json":"https://pith.science/api/pith-number/GV4PHCEDFR2LQAOOZ7LTNEZIPZ/graph.json","events_json":"https://pith.science/api/pith-number/GV4PHCEDFR2LQAOOZ7LTNEZIPZ/events.json","paper":"https://pith.science/paper/GV4PHCED"},"agent_actions":{"view_html":"https://pith.science/pith/GV4PHCEDFR2LQAOOZ7LTNEZIPZ","download_json":"https://pith.science/pith/GV4PHCEDFR2LQAOOZ7LTNEZIPZ.json","view_paper":"https://pith.science/paper/GV4PHCED","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.08216&json=true","fetch_graph":"https://pith.science/api/pith-number/GV4PHCEDFR2LQAOOZ7LTNEZIPZ/graph.json","fetch_events":"https://pith.science/api/pith-number/GV4PHCEDFR2LQAOOZ7LTNEZIPZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GV4PHCEDFR2LQAOOZ7LTNEZIPZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GV4PHCEDFR2LQAOOZ7LTNEZIPZ/action/storage_attestation","attest_author":"https://pith.science/pith/GV4PHCEDFR2LQAOOZ7LTNEZIPZ/action/author_attestation","sign_citation":"https://pith.science/pith/GV4PHCEDFR2LQAOOZ7LTNEZIPZ/action/citation_signature","submit_replication":"https://pith.science/pith/GV4PHCEDFR2LQAOOZ7LTNEZIPZ/action/replication_record"}},"created_at":"2026-05-18T01:11:52.530460+00:00","updated_at":"2026-05-18T01:11:52.530460+00:00"}