{"paper":{"title":"Statistical approximation by $(p,q)$-analogue of Bernstein-Stancu Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Asif Khan, Vinita Sharma","submitted_at":"2016-04-03T05:00:43Z","abstract_excerpt":"In this paper, some approximation properties of $(p,q)$-analogue of Bernstein-Stancu Operators has been studied. Rate of statistical convergence by means of modulus of continuity and Lipschitz type maximal functions has been investigated. Monotonicity of $(p,q)$-Bernstein-Stancu Operators and a global approximation theorem by means of Ditzian-Totik modulus of smoothness is established. A quantitative Voronovskaja type theorem is developed for these operators.\n  Furthermore, we show comparisons and some illustrative graphics for the convergence of operators to a function"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05339","kind":"arxiv","version":5},"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"}