{"paper":{"title":"On a functional equation related to two-variable weighted quasi-arithmetic means","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":"2017-06-27T20:38:12Z","abstract_excerpt":"In this paper, we are going to describe the solutions of the functional equation $$\n  \\varphi\\Big(\\frac{x+y}{2}\\Big)(f(x)+f(y))=\\varphi(x)f(x)+\\varphi(y)f(y) $$ concerning the unknown functions $\\varphi$ and $f$ defined on an open interval. In our main result only the continuity of the function $\\varphi$ and a regularity property of the set of zeroes of $f$ are assumed. As application, we determine the solutions of the functional equation $$\n  G(g(u)-g(v))=H(h(u)+h(v))+F(u)+F(v) $$ under monotonicity and differentiability conditions on the unknown functions $F,G,H,g,h$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09040","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"}