{"paper":{"title":"On strong $(\\alpha,\\F)$-convexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Judit Mak\\'o, Kazimierz Nikodem, Zsolt P\\'ales","submitted_at":"2012-12-04T21:58:50Z","abstract_excerpt":"In this paper, strongly $(\\alpha,T)$-convex functions, i.e., functions $f:D\\to \\R$ satisfying the functional inequality $$ f(tx+(1-t)y)\\leq tf(x)+(1-t)f(y)-t\\alpha\\big((1-t)(x-y)\\big)-(1-t)\\alpha\\big(t(y-x)\\big)$$ for $x,y\\in D$ and $t\\in T\\cap[0,1]$ are investigated. Here $D$ is a convex set in a linear space, $\\alpha$ is a nonnegative function on $D-D$, and $T\\subseteq\\R$ is a nonempty set. The main results provide various characterizations of strong $(\\alpha,T)$-convexity in the case when $T$ is a subfield of $\\R$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0887","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"}