{"paper":{"title":"A new variation on statistical ward continuity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Huseyin Cakalli","submitted_at":"2017-11-29T06:46:28Z","abstract_excerpt":"A real valued function defined on a subset $E$ of $\\mathbb{R}$, the set of real numbers, is $\\rho$-statistically downward continuous if it preserves $\\rho$-statistical downward quasi-Cauchy sequences of points in $E$, where a sequence $(\\alpha_{k})$ of real numbers is called ${\\rho}$-statistically downward quasi-Cauchy if $\\lim_{n\\rightarrow\\infty}\\frac{1}{\\rho_{n} }|\\{k\\leq n: \\Delta \\alpha_{k} \\geq \\varepsilon\\}|=0 $ for every $\\varepsilon>0$, in which $(\\rho_{n})$ is a non-decreasing sequence of positive real numbers tending to $\\infty$ such that $\\limsup _{n} \\frac{\\rho_{n}}{n}<\\infty $, $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10702","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"}