{"paper":{"title":"Solutions and stability of variant of Wilson's functional equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Elqorachi Elhoucien, Redouani Ahmed","submitted_at":"2015-05-14T10:14:51Z","abstract_excerpt":"In this paper we will investigate the solutions and stability of the generalized variant of Wilson's functional equation $$ (E):\\;\\;\\;\\; f(xy)+\\chi(y)f(\\sigma(y)x)=2f(x)g(y),\\; x,y\\in G,$$ where $G$ is a group, $\\sigma$ is an involutive morphism of $G$ and $\\chi$ is a character of $G$. (a) We solve $(E)$ when $\\sigma$ is an involutive automorphism, and we obtain some properties about solutions of $(E)$ when $\\sigma$ is an involutive anti-automorphism. (b) We obtain the Hyers Ulam stability of equation $(E)$. As an application, we prove the superstability of the functional equation $f(xy)+\\chi("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06512","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"}