{"paper":{"title":"On Kedlaya type inequalities for weighted means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Pawe{\\l} Pasteczka, Zsolt P\\'ales","submitted_at":"2017-11-09T17:46:11Z","abstract_excerpt":"In 2016 we proved that for every symmetric, repetition invariant and Jensen concave mean $\\mathscr{M}$ the Kedlaya-type inequality $$ \\mathscr{A}\\big(x_1,\\mathscr{M}(x_1,x_2),\\ldots,\\mathscr{M}(x_1,\\ldots,x_n)\\big)\\le \\mathscr{M} \\big(x_1, \\mathscr{A}(x_1,x_2),\\ldots,\\mathscr{A}(x_1,\\ldots,x_n)\\big) $$ holds for an arbitrary $(x_n)$ ($\\mathscr{A}$ stands for the arithmetic mean). We are going to prove the weighted counterpart of this inequality. More precisely, if $(x_n)$ is a vector with corresponding (non-normalized) weights $(\\lambda_n)$ and $\\mathscr{M}_{i=1}^n(x_i,\\lambda_i)$ denotes the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03493","kind":"arxiv","version":2},"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"}