{"paper":{"title":"Quantitative estimates in approximation by Bernstein-Durrmeyer-Choquet operators with respect to monotone and submodular set functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Sorin Gal","submitted_at":"2015-11-23T09:24:09Z","abstract_excerpt":"For the qualitative results of pointwise and uniform approximation obtained in \\cite{Gal-Opris}, we present general quantitative estimates in terms of the modulus of continuity and in terms of a $K$-functional, for the generalized multivariate Bernstein-Durrmeyer operator $M_{n, \\Gamma_{n, x}}$, written in terms of the Choquet integral with respect to a family of monotone and submodular set functions, $\\Gamma_{n, x}$, on the standard $d$-dimensional simplex. When $\\Gamma_{n, x}$ reduces to two elements, one a Choquet submodular set function and the other one a Borel measure, for suitable modif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03726","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"}