{"paper":{"title":"A class of functional equations on monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bouikhalene Belaid, Elqorachi Elhoucien","submitted_at":"2016-02-22T11:32:02Z","abstract_excerpt":"In \\cite{05} B. Ebanks and H. Stetk{\\ae}r obtained the solutions of the functional equation $f(xy)-f(\\sigma(y)x)=g(x)h(y)$ where $\\sigma$ is an involutive automorphism and $f,g,h$ are complex-valued functions, in the setting of a group $G$ and a monoid $M$.\n  Our main goal is to determine the complex-valued solutions of the following more general version of this equation, viz $f(xy)-\\mu(y)f(\\sigma(y)x)=g(x)h(y)$ where $\\mu: G\\longrightarrow \\mathbb{C}$ is a multiplicative function such that $\\mu(x\\sigma(x))=1$ for all $x\\in G$. As an application we find the complex-valued solutions $(f,g,h)$ o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02065","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"}