{"paper":{"title":"Characterizations of $(m,n)$-Jordan derivations on some algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Guangyu An, Jun He","submitted_at":"2018-03-06T07:43:07Z","abstract_excerpt":"Let $\\mathcal R$ be a ring, $\\mathcal{M}$ be a $\\mathcal R$-bimodule and $m,n$ be two fixed nonnegative integers with $m+n\\neq0$. An additive mapping $\\delta$ from $\\mathcal R$ into $\\mathcal{M}$ is called an \\emph{$(m,n)$-Jordan derivation} if $(m+n)\\delta(A^{2})=2mA\\delta(A)+2n\\delta(A)A$ for every $A$ in $\\mathcal R$. In this paper, we prove that every $(m,n)$-Jordan derivation from a $C^{*}$-algebra into its Banach bimodule is zero. An additive mapping $\\delta$ from $\\mathcal R$ into $\\mathcal{M}$ is called a $(m,n)$-Jordan derivable mapping at $W$ in $\\mathcal R$ if $(m+n)\\delta(AB+BA)=2m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02046","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"}