{"paper":{"title":"A new invariance identity and means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Janusz Matkowski, Jimmy Devillet","submitted_at":"2018-07-12T20:31:16Z","abstract_excerpt":"The invariance identity involving three operations $D_{f,g}:X\\times X\\rightarrow X$ of the form \\begin{equation*} D_{f,g}\\left( x,y\\right) =\\left( f\\circ g\\right) ^{-1}\\left( f\\left( x\\right) \\oplus g\\left( y\\right) \\right) \\text{,} \\end{equation*} is proposed. The connections of these operations with means is investigated. The question when the invariance equality admits three means leads to a composite functional equation. Problem to determine its continuous solutions is posed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04811","kind":"arxiv","version":3},"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"}