{"paper":{"title":"An extensions of Kannappan's and Van Vleck's functional equations on semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Elqorachi Elhoucien, Redouani Ahmed","submitted_at":"2016-11-16T11:15:04Z","abstract_excerpt":"This paper treats two functional equations, the Kannppan-Van Vleck functional equation $$\\mu(y)f(x\\tau(y)z_0)\\pm f(xyz_0) =2f(x)f(y), \\;x,y\\in S$$ and the following variant of it\n  $$\\mu(y)f(\\tau(y)xz_0)\\pm f(xyz_0) = 2f(x)f(y), \\;x,y\\in S,$$ in the setting of semigroups $S$ that need not be abelian or unital, $\\tau$ is an involutive morphism of $S$, $\\mu$ : $S\\longrightarrow \\mathbb{C}$ is a multiplicative function such that $\\mu(x\\tau(x))=1$ for all $x\\in S$ and $z_0$ is a fixed element in the center of $S$. We find the complex-valued solutions of these equations in terms of multiplicative f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06861","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"}