{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:MIRTMCI2PZS3FWMXEAODUUP5E2","short_pith_number":"pith:MIRTMCI2","schema_version":"1.0","canonical_sha256":"622336091a7e65b2d997201c3a51fd2695089570e83dcc75209b72006f80ece7","source":{"kind":"arxiv","id":"1709.04700","version":3},"attestation_state":"computed","paper":{"title":"On proximal mappings with Young functions in uniformly convex Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.FA","authors_text":"Miroslav Bacak, Ulrich Kohlenbach","submitted_at":"2017-09-14T11:07:06Z","abstract_excerpt":"It is well known in convex analysis that proximal mappings on Hilbert spaces are $1$-Lipschitz. In the present paper we show that proximal mappings on uniformly convex Banach spaces are uniformly continuous on bounded sets. Moreover, we introduce a new general proximal mapping whose regularization term is given as a composition of a Young function and the norm, and formulate our results at this level of generality. It is our aim to obtain the corresponding modulus of uniform continuity explicitly in terms of a modulus of uniform convexity of the norm and of moduli witnessing properties of the "},"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":"1709.04700","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-09-14T11:07:06Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"ba464a6545b9df23f1a3d518be9ebd075fbac472e9c5d202470850f0f11f3125","abstract_canon_sha256":"c52922ac606e084221537d34797ad73ff366a3a421a9cc982dc271b2cedf7d2b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:18.700697Z","signature_b64":"EchQXC0u1Ac3GmtlgmjzZXfuFu+4Wq2G8rn305NAzQUlOcpAURz9IYikW/0NcBeiZdFpFVf7FRL33ZlooTsACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"622336091a7e65b2d997201c3a51fd2695089570e83dcc75209b72006f80ece7","last_reissued_at":"2026-05-18T00:31:18.699938Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:18.699938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On proximal mappings with Young functions in uniformly convex Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.FA","authors_text":"Miroslav Bacak, Ulrich Kohlenbach","submitted_at":"2017-09-14T11:07:06Z","abstract_excerpt":"It is well known in convex analysis that proximal mappings on Hilbert spaces are $1$-Lipschitz. In the present paper we show that proximal mappings on uniformly convex Banach spaces are uniformly continuous on bounded sets. Moreover, we introduce a new general proximal mapping whose regularization term is given as a composition of a Young function and the norm, and formulate our results at this level of generality. It is our aim to obtain the corresponding modulus of uniform continuity explicitly in terms of a modulus of uniform convexity of the norm and of moduli witnessing properties of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04700","kind":"arxiv","version":3},"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":"1709.04700","created_at":"2026-05-18T00:31:18.700051+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.04700v3","created_at":"2026-05-18T00:31:18.700051+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04700","created_at":"2026-05-18T00:31:18.700051+00:00"},{"alias_kind":"pith_short_12","alias_value":"MIRTMCI2PZS3","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"MIRTMCI2PZS3FWMX","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"MIRTMCI2","created_at":"2026-05-18T12:31:31.346846+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/MIRTMCI2PZS3FWMXEAODUUP5E2","json":"https://pith.science/pith/MIRTMCI2PZS3FWMXEAODUUP5E2.json","graph_json":"https://pith.science/api/pith-number/MIRTMCI2PZS3FWMXEAODUUP5E2/graph.json","events_json":"https://pith.science/api/pith-number/MIRTMCI2PZS3FWMXEAODUUP5E2/events.json","paper":"https://pith.science/paper/MIRTMCI2"},"agent_actions":{"view_html":"https://pith.science/pith/MIRTMCI2PZS3FWMXEAODUUP5E2","download_json":"https://pith.science/pith/MIRTMCI2PZS3FWMXEAODUUP5E2.json","view_paper":"https://pith.science/paper/MIRTMCI2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.04700&json=true","fetch_graph":"https://pith.science/api/pith-number/MIRTMCI2PZS3FWMXEAODUUP5E2/graph.json","fetch_events":"https://pith.science/api/pith-number/MIRTMCI2PZS3FWMXEAODUUP5E2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MIRTMCI2PZS3FWMXEAODUUP5E2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MIRTMCI2PZS3FWMXEAODUUP5E2/action/storage_attestation","attest_author":"https://pith.science/pith/MIRTMCI2PZS3FWMXEAODUUP5E2/action/author_attestation","sign_citation":"https://pith.science/pith/MIRTMCI2PZS3FWMXEAODUUP5E2/action/citation_signature","submit_replication":"https://pith.science/pith/MIRTMCI2PZS3FWMXEAODUUP5E2/action/replication_record"}},"created_at":"2026-05-18T00:31:18.700051+00:00","updated_at":"2026-05-18T00:31:18.700051+00:00"}