{"paper":{"title":"Shape preserving properties of generalized Bernstein operators on Extended Chebyshev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"H. Render, J. M. Aldaz, O. Kounchev","submitted_at":"2008-05-12T12:00:15Z","abstract_excerpt":"We study the existence and shape preserving properties of a generalized Bernstein operator $B_{n}$ fixing a strictly positive function $f_{0}$, and a second function $f_{1}$ such that $f_{1}/f_{0}$ is strictly increasing, within the framework of extended Chebyshev spaces $U_{n}$. The first main result gives an inductive criterion for existence: suppose there exists a Bernstein operator $B_{n}:C[a,b]\\to U_{n}$ with strictly increasing nodes, fixing $f_{0}, f_{1}\\in U_{n}$. If $U_{n}\\subset U_{n + 1}$ and $U_{n + 1}$ has a non-negative Bernstein basis, then there exists a Bernstein operator $B_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.1614","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"}