{"paper":{"title":"Convexity with respect to families of means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Gyula Maksa, Zsolt P\\'ales","submitted_at":"2015-12-22T21:45:15Z","abstract_excerpt":"In this paper we investigate continuity properties of functions $f:\\mathbb{R}_+\\to\\mathbb{R}_+$ that satisfy the $(p,q)$-Jensen convexity inequality $$ f\\big(H_p(x,y)\\big)\\leq H_q(f(x),f(y)) \\qquad(x,y>0), $$ where $H_p$ stands for the $p$th power (or H\\\"older) mean. One of the main results shows that there exist discontinuous multiplicative functions that are $(p,p)$-Jensen convex for all positive rational number $p$. A counterpart of this result states that if $f$ is $(p,p)$-Jensen convex for all $p\\in P\\subseteq\\mathbb{R}_+$, where $P$ is a set of positive Lebesgue measure, then $f$ must be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07272","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"}