{"paper":{"title":"On approximate ternary m-derivations and $\\sigma$-homomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. G. Ghazanfari, Z. Alizadeh","submitted_at":"2015-06-08T15:10:57Z","abstract_excerpt":"In this paper we introduce ternary modules over ternary algebras and using fixed point methods, we prove the stability and super-stability of ternary additive, quadratic, cubic and quartic derivations and $\\sigma$-homomorphisms in such structures for the functional equation \\begin{equation*} \\begin{split} &\\quad f(ax+y)+f(ax-y)= a^{m-2}[f(x+y)+f(x-y)]\\\\&+2(a^2-1)[a^{m-2}f(x)+\\frac{(m-2)(1-(m-2)^2)}{6}f(y)]. \\end{split} \\end{equation*} for each $m=1,2,3,4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02536","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"}