{"paper":{"title":"On functional inequalities associated with Drygas functional equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Elqorachi Elhoucien, Manar Youssef","submitted_at":"2014-05-21T17:35:12Z","abstract_excerpt":"In the paper, the equivalence of the functional inequality $$\\|2f(x)+f(y)+f(-y)-f(x-y)\\|\\leq\\|f(x+y)\\|\\;\\;\\;(x,y\\in{G})$$ and the Drygas functional equation $$f(x+y)+f(x-y)=2f(x)+f(y)+f(-y)\\;\\;\\;(x,y\\in{G})$$ is proved for functions $f:G\\rightarrow E$ where $(G, +)$ is an abelian group, $(E, <\\cdot, \\cdot>)$ is an inner product space, and the norm is derived from the inner product in the usual way."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7942","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"}