{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:2JRC2FWRZYYHDNYWHDNGNVJ2GI","short_pith_number":"pith:2JRC2FWR","schema_version":"1.0","canonical_sha256":"d2622d16d1ce3071b71638da66d53a323389708434e82725d92798cfd2564d14","source":{"kind":"arxiv","id":"1201.4475","version":1},"attestation_state":"computed","paper":{"title":"Biholomorphic Convex Mappings of Order alpha on the Unit Ball in Hilbert Spaces","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Ming-Sheng Liu, Yu-Can Zhu","submitted_at":"2012-01-21T14:22:32Z","abstract_excerpt":"In this paper, we first introduce the concept of biholomorphic convex mapping of order alpha on the unit ball B in a complex Hilbert space X. Next we provide some sufficient conditions that a locally biholomorphic mapping f is a biholomorphic convex mapping of order alpha and give an Alexander's theorem between the subclass of convex mappings and the subclass of starlike mappings on B in Hilbert space. We also obtain the order of starlikeness of biholomorphic convex mappings of order alpha on B in Hilbert spaces. Finally, we construct some concrete examples of biholomorphic convex mappings of "},"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":"1201.4475","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CV","submitted_at":"2012-01-21T14:22:32Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"5fca04cac192c0168449053ff465e7917e122e3465c53313f41fa8fdd18dd66e","abstract_canon_sha256":"dc830bd3e127361b9bdb1788c49ec13e9698ca1910d898f6588c5f04ccdc986f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:05.945125Z","signature_b64":"vjErf9xok2w7W0iDSD3Rf3rZB0qBuZz/sPEFcQlPxeTWnEUpgtyK+ZvFqrNyIEcOMVIaYix8x0Wt0LxXqOHlDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2622d16d1ce3071b71638da66d53a323389708434e82725d92798cfd2564d14","last_reissued_at":"2026-05-18T04:04:05.944693Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:05.944693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Biholomorphic Convex Mappings of Order alpha on the Unit Ball in Hilbert Spaces","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Ming-Sheng Liu, Yu-Can Zhu","submitted_at":"2012-01-21T14:22:32Z","abstract_excerpt":"In this paper, we first introduce the concept of biholomorphic convex mapping of order alpha on the unit ball B in a complex Hilbert space X. Next we provide some sufficient conditions that a locally biholomorphic mapping f is a biholomorphic convex mapping of order alpha and give an Alexander's theorem between the subclass of convex mappings and the subclass of starlike mappings on B in Hilbert space. We also obtain the order of starlikeness of biholomorphic convex mappings of order alpha on B in Hilbert spaces. Finally, we construct some concrete examples of biholomorphic convex mappings of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4475","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":"1201.4475","created_at":"2026-05-18T04:04:05.944757+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.4475v1","created_at":"2026-05-18T04:04:05.944757+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4475","created_at":"2026-05-18T04:04:05.944757+00:00"},{"alias_kind":"pith_short_12","alias_value":"2JRC2FWRZYYH","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"2JRC2FWRZYYHDNYW","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"2JRC2FWR","created_at":"2026-05-18T12:26:50.516681+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/2JRC2FWRZYYHDNYWHDNGNVJ2GI","json":"https://pith.science/pith/2JRC2FWRZYYHDNYWHDNGNVJ2GI.json","graph_json":"https://pith.science/api/pith-number/2JRC2FWRZYYHDNYWHDNGNVJ2GI/graph.json","events_json":"https://pith.science/api/pith-number/2JRC2FWRZYYHDNYWHDNGNVJ2GI/events.json","paper":"https://pith.science/paper/2JRC2FWR"},"agent_actions":{"view_html":"https://pith.science/pith/2JRC2FWRZYYHDNYWHDNGNVJ2GI","download_json":"https://pith.science/pith/2JRC2FWRZYYHDNYWHDNGNVJ2GI.json","view_paper":"https://pith.science/paper/2JRC2FWR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.4475&json=true","fetch_graph":"https://pith.science/api/pith-number/2JRC2FWRZYYHDNYWHDNGNVJ2GI/graph.json","fetch_events":"https://pith.science/api/pith-number/2JRC2FWRZYYHDNYWHDNGNVJ2GI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2JRC2FWRZYYHDNYWHDNGNVJ2GI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2JRC2FWRZYYHDNYWHDNGNVJ2GI/action/storage_attestation","attest_author":"https://pith.science/pith/2JRC2FWRZYYHDNYWHDNGNVJ2GI/action/author_attestation","sign_citation":"https://pith.science/pith/2JRC2FWRZYYHDNYWHDNGNVJ2GI/action/citation_signature","submit_replication":"https://pith.science/pith/2JRC2FWRZYYHDNYWHDNGNVJ2GI/action/replication_record"}},"created_at":"2026-05-18T04:04:05.944757+00:00","updated_at":"2026-05-18T04:04:05.944757+00:00"}