{"paper":{"title":"Yet another look at positive linear operators, $q$-monotonicity and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.NA"],"primary_cat":"math.CA","authors_text":"A. Prymak, D. Leviatan, I. A. Shevchuk, K. Kopotun","submitted_at":"2016-02-23T21:04:51Z","abstract_excerpt":"For each $q\\in{\\mathbb{N}}_0$, we construct positive linear polynomial approximation operators $M_n$ that simultaneously preserve $k$-monotonicity for all $0\\leq k\\leq q$ and yield the estimate \\[ |f(x)-M_n(f, x)| \\leq c \\omega_2^{\\varphi^\\lambda} \\left(f, n^{-1} \\varphi^{1-\\lambda/2}(x) \\left(\\varphi(x) + 1/n \\right)^{-\\lambda/2} \\right) , \\] for $x\\in [0,1]$ and $\\lambda\\in [0, 2)$, where $\\varphi(x) := \\sqrt{x(1-x)}$ and $\\omega_2^{\\psi}$ is the second Ditzian-Totik modulus of smoothness corresponding to the \"step-weight function\" $\\psi$.\n  In particular, this implies that the rate of best "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07313","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"}