{"paper":{"title":"The distance between two limit $q$-Bernstein operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mehmet Turan, Sofiya Ostrovska","submitted_at":"2017-08-25T09:53:11Z","abstract_excerpt":"For $q\\in(0,1),$ let $B_q$ denote the limit $q$-Bernstein operator. In this paper, the distance between $B_q$ and $B_r$ for distinct $q$ and $r$ in the operator norm on $C[0,1]$ is estimated, and it is proved that $1\\leqslant \\|B_q-B_r\\|\\leqslant 2,$ where both of the equalities can be attained. To elaborate more, the distance depends on whether or not $r$ and $q$ are rational powers of each other. For example, if $r^j\\neq q^m$ for all $j,m\\in \\mathbb{N},$ then $\\|B_q-B_r\\|=2,$ and if $r=q^m, m\\in \\mathbb{N},$ then $\\|B_q-B_r\\|=2(m-1)/m.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07669","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"}