{"paper":{"title":"Approximately bisectrix-orthogonality preserving mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ali Zamani","submitted_at":"2015-06-20T09:31:03Z","abstract_excerpt":"Regarding the geometry of a real normed space ${\\mathcal X}$, we mainly introduce a notion of approximate bisectrix-orthogonality on vectors $x, y \\in {\\mathcal X}$ as follows: $${x\\np{\\varepsilon}}_W y \\mbox{if and only if} \\sqrt{2}\\frac{1-\\varepsilon}{1+\\varepsilon}\\|x\\|\\,\\|y\\|\\leq \\Big\\|\\,\\|y\\|x+\\|x\\|y\\,\\Big\\|\\leq\\sqrt{2}\\frac{1+\\varepsilon}{1-\\varepsilon}\\|x\\|\\,\\|y\\|.$$ We study class of linear mappings preserving the approximately bisectrix-orthogonality ${\\np{\\varepsilon}}_W$. In particular, we show that if $T: {\\mathcal X}\\to {\\mathcal Y}$ is an approximate linear similarity, then $${x\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06218","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"}