{"paper":{"title":"Continuity of modulus of noncompact convexity for minimalizable measures of noncompactness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Amra Rekic-Vukovic, Ivan Arandjelovic, Nermin Okicic, Vedad Pasic","submitted_at":"2016-06-03T12:40:42Z","abstract_excerpt":"We consider the modulus of noncompact convexity $\\Delta_{X,\\phi}(\\varepsilon)$ associated with the minimalizable measure of noncompactness $\\phi$. We present some properties of this modulus, while the main result of this paper is showing that $\\Delta_{X,\\phi }(\\varepsilon)$ is a subhomogenous and continuous function on $[0,\\phi (\\bar{B}_X))$ for an arbitrary minimalizable measure of compactness $\\phi$ in the case of a Banach space $X$ with the Radon-Nikodym property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01063","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"}