{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ZTM52GNVSXEFDK2EBMC3RZ3B6G","short_pith_number":"pith:ZTM52GNV","schema_version":"1.0","canonical_sha256":"ccd9dd19b595c851ab440b05b8e761f1810a575e53d09b7e1eba6bda8003483f","source":{"kind":"arxiv","id":"1802.08476","version":2},"attestation_state":"computed","paper":{"title":"The asymptotic behaviour of convex combinations of firmly nonexpansive mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.LO"],"primary_cat":"math.OC","authors_text":"Andrei Sipos","submitted_at":"2018-02-23T10:51:20Z","abstract_excerpt":"We show that in the framework of CAT(0) spaces, any convex combination of two mappings which are firmly nonexpansive -- or which satisfy the more general property $(P_2)$ -- is asymptotically regular, conditional on its fixed point set being nonempty, and, in addition, also $\\Delta$-convergent to such a fixed point. These results are established by the construction and study of a convex combination metric on the Cartesian square of a CAT(0) space. We also derive a uniform rate of asymptotic regularity in the sense of proof mining. All these results are then interpreted in the special case of t"},"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":"1802.08476","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-23T10:51:20Z","cross_cats_sorted":["math.FA","math.LO"],"title_canon_sha256":"702b4f08ae5670de190aa706fc258dfbbc732e77e934c68a13728ebd3618438e","abstract_canon_sha256":"31472df6f1a2d0a752f9905298e02a13a3e35e678c3db90c02fcfebdc9bff9b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:22.897969Z","signature_b64":"LnMc2YkWHNWrBSi7aGH54hvMbrBLlOlJvcJyMXGU2Oh3VBT+SQ2B5nOycEZbkpvynJ4B9hnXUdx3zBMyIhkVDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccd9dd19b595c851ab440b05b8e761f1810a575e53d09b7e1eba6bda8003483f","last_reissued_at":"2026-05-17T23:59:22.897620Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:22.897620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The asymptotic behaviour of convex combinations of firmly nonexpansive mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.LO"],"primary_cat":"math.OC","authors_text":"Andrei Sipos","submitted_at":"2018-02-23T10:51:20Z","abstract_excerpt":"We show that in the framework of CAT(0) spaces, any convex combination of two mappings which are firmly nonexpansive -- or which satisfy the more general property $(P_2)$ -- is asymptotically regular, conditional on its fixed point set being nonempty, and, in addition, also $\\Delta$-convergent to such a fixed point. These results are established by the construction and study of a convex combination metric on the Cartesian square of a CAT(0) space. We also derive a uniform rate of asymptotic regularity in the sense of proof mining. All these results are then interpreted in the special case of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08476","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1802.08476","created_at":"2026-05-17T23:59:22.897673+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.08476v2","created_at":"2026-05-17T23:59:22.897673+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08476","created_at":"2026-05-17T23:59:22.897673+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZTM52GNVSXEF","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZTM52GNVSXEFDK2E","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZTM52GNV","created_at":"2026-05-18T12:33:07.085635+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/ZTM52GNVSXEFDK2EBMC3RZ3B6G","json":"https://pith.science/pith/ZTM52GNVSXEFDK2EBMC3RZ3B6G.json","graph_json":"https://pith.science/api/pith-number/ZTM52GNVSXEFDK2EBMC3RZ3B6G/graph.json","events_json":"https://pith.science/api/pith-number/ZTM52GNVSXEFDK2EBMC3RZ3B6G/events.json","paper":"https://pith.science/paper/ZTM52GNV"},"agent_actions":{"view_html":"https://pith.science/pith/ZTM52GNVSXEFDK2EBMC3RZ3B6G","download_json":"https://pith.science/pith/ZTM52GNVSXEFDK2EBMC3RZ3B6G.json","view_paper":"https://pith.science/paper/ZTM52GNV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.08476&json=true","fetch_graph":"https://pith.science/api/pith-number/ZTM52GNVSXEFDK2EBMC3RZ3B6G/graph.json","fetch_events":"https://pith.science/api/pith-number/ZTM52GNVSXEFDK2EBMC3RZ3B6G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZTM52GNVSXEFDK2EBMC3RZ3B6G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZTM52GNVSXEFDK2EBMC3RZ3B6G/action/storage_attestation","attest_author":"https://pith.science/pith/ZTM52GNVSXEFDK2EBMC3RZ3B6G/action/author_attestation","sign_citation":"https://pith.science/pith/ZTM52GNVSXEFDK2EBMC3RZ3B6G/action/citation_signature","submit_replication":"https://pith.science/pith/ZTM52GNVSXEFDK2EBMC3RZ3B6G/action/replication_record"}},"created_at":"2026-05-17T23:59:22.897673+00:00","updated_at":"2026-05-17T23:59:22.897673+00:00"}