{"paper":{"title":"On $\\varphi$-convexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Judit Mak\\'o, Zsolt P\\'ales","submitted_at":"2012-11-19T21:31:54Z","abstract_excerpt":"In this paper, approximate convexity and approximate midconvexity properties, called $\\varphi$-convexity and $\\varphi$-midconvexity, of real valued function are investigated. Various characterizations of $\\varphi$-convex and $\\varphi$-midconvex functions are obtained. Furthermore, the relationship between $\\varphi$-midconvexity and $\\varphi$-convexity is established."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4599","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"}