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We call such estimates \"interpolatory estimates\".\n  In 1985, DeVore and Yu were the first to obtain this kind of results for monotone polynomial approximation.\n  Their estimates involved the second modulus of smoothness $\\omega_2(f,\\cdot)$ of $f$ evaluated at $\\sqrt"},"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":"1711.07083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-11-19T21:17:36Z","cross_cats_sorted":[],"title_canon_sha256":"8d56502f7a39d0fa7e56bc5f1ab1200bb4d7f2a890eca23ef047e9472022ecdd","abstract_canon_sha256":"f533326e2ce9a5eac71552c207b1d59d64fe5c25db6792d8b2f56354abeb01ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:12.318078Z","signature_b64":"2oQ6no5gVv8ubLgjkO87p/JNqiuTC6sTNQRRJkLWFn81i7I/2y4UWeBW/dLBnKCLZfS8wTDlkSRoSV5h5+ALAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f736c7919b8677622aebba70dfee7d035cccd548132f726171317f8d2496cdc","last_reissued_at":"2026-05-18T00:30:12.317289Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:12.317289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Interpolatory pointwise estimates for monotone polynomial approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"D. 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