{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T16:12:19Z","timestamp":1777479139388,"version":"3.51.4"},"reference-count":12,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2024,8,1]],"date-time":"2024-08-01T00:00:00Z","timestamp":1722470400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-sa\/3.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,8,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>This article extends the formalization of the theory of differentiation in real normed spaces in the Mizar system. The focus is on higher-order derivatives and the inverse function theorem. Additionally, we encode the differentiability of the inversion operator on invertible linear operators.<\/jats:p>","DOI":"10.2478\/forma-2024-0021","type":"journal-article","created":{"date-parts":[[2025,1,3]],"date-time":"2025-01-03T14:07:37Z","timestamp":1735913257000},"page":"247-269","source":"Crossref","is-referenced-by-count":1,"title":["Higher-Order Differentiation and Inverse Function Theorem in Real Normed Spaces"],"prefix":"10.2478","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1110-4342","authenticated-orcid":false,"given":"Kazuhisa","family":"Nakasho","sequence":"first","affiliation":[{"name":"Yamaguchi University , Yamaguchi , Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yasunari","family":"Shidama","sequence":"additional","affiliation":[{"name":"Karuizawa Hotch 244-1 Nagano , Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2024,12,31]]},"reference":[{"key":"2026042801415219970_j_forma-2024-0021_ref_001","doi-asserted-by":"crossref","unstructured":"Grzegorz Bancerek, Czes\u0142aw Byli\u0144ski, Adam Grabowski, Artur Korni\u0142owicz, Roman Matuszewski, Adam Naumowicz, Karol P\u0105k, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261\u2013279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007\/978-3-319-20615-8_17.","DOI":"10.1007\/978-3-319-20615-8_17"},{"key":"2026042801415219970_j_forma-2024-0021_ref_002","doi-asserted-by":"crossref","unstructured":"Grzegorz Bancerek, Czes\u0142aw Byli\u0144ski, Adam Grabowski, Artur Korni\u0142owicz, Roman Matuszewski, Adam Naumowicz, and Karol P\u0105k. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9\u201332, 2018. doi:10.1007\/s10817-017-9440-6.","DOI":"10.1007\/s10817-017-9440-6"},{"key":"2026042801415219970_j_forma-2024-0021_ref_003","unstructured":"Nelson Dunford and Jacob T. Schwartz. Linear operators I. 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Hermann, 1997."},{"key":"2026042801415219970_j_forma-2024-0021_ref_011","unstructured":"Laurent Schwartz. Calcul diff\u00e9rentiel, tome 2. Analyse. Hermann, 1997."},{"key":"2026042801415219970_j_forma-2024-0021_ref_012","unstructured":"K\u00f4saku Yosida. Functional Analysis. 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