{"paper":{"title":"Implications between generalized convexity properties of real functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Tibor Kiss, Zsolt P\\'ales","submitted_at":"2015-07-19T14:45:25Z","abstract_excerpt":"Motivated by the well-known implications among $t$-convexity properties of real functions, analogous relations among the upper and lower $M$-convexity properties of real functions are established. More precisely, having an $n$-tuple $(M_1,\\dots,M_n)$ of continuous two-variable means, the notion of the descendant of these means (which is also an $n$-tuple $(N_1,\\dots,N_n)$ of two-variable means) is introduced. In particular, when all the means $M_i$ are weighted arithmetic, then the components of their descendants are also weighted arithmetic means. More general statements are obtained in terms"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05295","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"}