{"paper":{"title":"On the local and global comparison of generalized Bajraktarevi\\'c means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Amr Zakaria, Zsolt P\\'ales","submitted_at":"2017-03-07T12:35:38Z","abstract_excerpt":"Given two continuous functions $f,g:I\\to\\mathbb{R}$ such that $g$ is positive and $f/g$ is strictly monotone, a measurable space $(T,A)$, a measurable family of $d$-variable means $m: I^d\\times T\\to I$, and a probability measure $\\mu$ on the measurable sets $A$, the $d$-variable mean $M_{f,g,m;\\mu}:I^d\\to I$ is defined by $$\n  M_{f,g,m;\\mu}(\\pmb{x})\n  :=\\left(\\frac{f}{g}\\right)^{-1}\\left(\n  \\frac{\\int_T f\\big(m(x_1,\\dots,x_d,t)\\big) d\\mu(t)}\n  {\\int_T g\\big(m(x_1,\\dots,x_d,t)\\big) d\\mu(t)}\\right)\n  \\qquad(\\pmb{x}=(x_1,\\dots,x_d)\\in I^d). $$ The aim of this paper is to study the local and globa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02354","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"}