{"paper":{"title":"Solutions and stability of generalized Kannappan's and Van Vleck's functional equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Elqorachi Elhoucien, Redouani Ahmed","submitted_at":"2016-07-12T10:49:44Z","abstract_excerpt":"We study the solutions of the integral Kannappan's and Van Vleck's functional equations $$\\int_{S}f(xyt)d\\mu(t)+\\int_{S}f(x\\sigma(y)t)d\\mu(t) = 2f(x)f(y), \\;x,y\\in S;$$ $$\\int_{S}f( x\\sigma(y)t)d\\mu(t)-\\int_{S}f(xyt)d\\mu(t) = 2f(x)f(y), \\;x,y\\in S,$$ where $S$ is a semigroup, $\\sigma$ is an involutive automorphism of $S$ and $\\mu$ is a linear combination of Dirac measures $(\\delta_{z_{i}})_{i\\in I}$, such that for all $i\\in I$, $z_{i}$ is contained in the center of $S$. We show that the solutions of these equations are closely related to the solutions of the d'Alembert's classic functional equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05166","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"}