{"paper":{"title":"On Abel statistical convergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Huseyin Cakalli, Iffet Taylan","submitted_at":"2017-11-27T07:29:13Z","abstract_excerpt":"In this paper, we introduce and investigate a concept of Abel statistical continuity. A real valued function $f$ is Abel statistically continuous on a subset $E$ of $\\R$, the set of real numbers, if it preserves Abel statistical convergent sequences, i.e. $(f(p_{k}))$ is Abel statistically convergent whenever $(p_{k})$ is an Abel statistical convergent sequence of points in $E$, where a sequence $(p_{k})$ of point in $\\R$ is called Abel statistically convergent to a real number $L$ if Abel density of the set $\\{k\\in{\\N}: |p_{k}-L|\\geq\\varepsilon \\}$ is $0$ for every $\\varepsilon>0$. Some other"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09563","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"}