{"paper":{"title":"On the Approximation Properties of Ces\\`{a}ro Means of Negative Order of double Vilenkin-Fourier Series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tsitsino Tepnadze","submitted_at":"2018-11-15T15:22:46Z","abstract_excerpt":"In this paper we establish approximation properties of Ces\\`{a}ro $% (C,-\\alpha ,-\\beta )$ means with $\\alpha ,\\beta $ $\\epsilon $ $(0,1)$ of Vilenkin-Fourier series.This result allows one to obtain a condition which is sufficient for the convergence of the means $\\sigma _{n,m}^{-\\alpha ,-\\beta }(x,y,f)$ to $f(x,y)$ in the $L^{p}-$metric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07705","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"}