{"paper":{"title":"On Seiffert-like means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alfred Witkowski","submitted_at":"2013-09-05T07:12:25Z","abstract_excerpt":"We investigate the representation of homogeneous, symmetric means in the form M(x,y)=\\frac{x-y}{2f((x-y)/(x+y))}. This allows for a new approach to comparing means. As an example, we provide optimal estimate of the form (1-\\mu)min(x,y)+ \\mu max(x,y)<= M(x,y)<= (1-\\nu)min(x,y)+ \\nu max(x,y) and M((x+y)/2-\\mu(x-y)/2,(x+y)/2+\\mu(x-y)/2)<= N(x,y)<= M((x+y)/2-\\nu(x-y)/2,(x+y)/2+\\nu(x-y)/2) for some known means."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1244","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"}