{"paper":{"title":"A notion of $\\alpha\\beta$-statistical convergence of order $\\gamma$ in probability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pratulananda Das, Sanjoy Ghosal, Sumit Som, Vatan Karakaya","submitted_at":"2016-05-20T11:48:56Z","abstract_excerpt":"A sequence of real numbers $\\{x_{n}\\}_{n\\in \\mathbb{N}}$ is said to be $\\alpha \\beta$-statistically convergent of order $\\gamma$ (where $0<\\gamma\\leq 1$) to a real number $x$ \\cite{a} if for every $\\delta>0,$ $$\\underset{n\\rightarrow \\infty} {\\lim} \\frac{1}{(\\beta_{n} - \\alpha_{n} + 1)^\\gamma}~ |\\{k \\in [\\alpha_n,\\beta_n] : |x_{k}-x|\\geq \\delta \\}|=0.$$ where $\\{\\alpha_{n}\\}_{n\\in \\mathbb{N}}$ and $\\{\\beta_{n}\\}_{n\\in \\mathbb{N}}$ be two sequences of positive real numbers such that $\\{\\alpha_{n}\\}_{n\\in \\mathbb{N}}$ and $\\{\\beta_{n}\\}_{n\\in \\mathbb{N}}$ are both non-decreasing, $\\beta_{n}\\geq "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06302","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"}