{"paper":{"title":"Stability of Euler-Lagrange type cubic functional equations in quasi-Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anurak Thanyacharoen, Nguyen Van Dung, Wutiphol Sintunavarat","submitted_at":"2019-06-07T11:08:43Z","abstract_excerpt":"In this paper, we study the generalized Hyers-Ulam stability of Euler-Lagrange type cubic functional equation of the form \\begin{align*} 2mf(x + my) + 2f(mx - y) = (m^3 + m)[f(x+ y) + f(x - y)] + 2(m^4 - 1)f(y) \\end{align*} for all $x,y \\in X$, where $m$ is a fixed scalar such that $m \\neq 0,1$, and $f$ is a map from a quasi-normed space $X$ to a quasi-Banach space $Y$ over the same field with $X$ by applying the alternative fixed point theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03010","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"}