{"paper":{"title":"Cubic Derivations on Banach Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Abasalt Bodaghi","submitted_at":"2013-01-14T08:59:50Z","abstract_excerpt":"Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule. A mapping $D :A\\longrightarrow X$ is a cubic derivation if $D$ is a cubic homogeneous mapping, that is $D$ is cubic and $D(\\lambda a)={\\lambda}^3 D(a)$ for any complex number $\\lambda$ and all $a\\in A$, and $D(ab)=D(a)\\cdot b^3 +a^3\\cdot D(b)$ for all $a,b\\in A$. In this paper, we prove the stability of a cubic derivation with direct method. We also employ a fixed point method to establish of the stability and the superstability for cubic derivations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2888","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"}