{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T13:51:17Z","timestamp":1777470677877,"version":"3.51.4"},"reference-count":12,"publisher":"Walter de Gruyter GmbH","issue":"3","license":[{"start":{"date-parts":[[2022,10,1]],"date-time":"2022-10-01T00:00:00Z","timestamp":1664582400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,10,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>Previous Mizar articles [7, 6, 5] formalized the implicit and inverse function theorems for Frechet continuously differentiable maps on Banach spaces. In this paper, using the Mizar system [1], [2], we formalize these theorems on Euclidean spaces by specializing them. We referred to [4], [12], [10], [11] in this formalization.<\/jats:p>","DOI":"10.2478\/forma-2022-0012","type":"journal-article","created":{"date-parts":[[2022,12,30]],"date-time":"2022-12-30T13:08:28Z","timestamp":1672405708000},"page":"159-168","source":"Crossref","is-referenced-by-count":3,"title":["On Implicit and Inverse Function Theorems on Euclidean Spaces"],"prefix":"10.2478","volume":"30","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":[[2022,12,30]]},"reference":[{"key":"2026042801401829038_j_forma-2022-0012_ref_001","doi-asserted-by":"crossref","unstructured":"[1] Grzegorz Bancerek, Czes\u0142aw Bylinacute;ski, 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":"2026042801401829038_j_forma-2022-0012_ref_002","doi-asserted-by":"crossref","unstructured":"[2] Grzegorz Bancerek, Czes\u0142aw Bylinacute;ski, 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\/s10817-017-9440-6.10.1007\/s10817-017-9440-6604425130069070","DOI":"10.1007\/s10817-017-9440-6"},{"key":"2026042801401829038_j_forma-2022-0012_ref_003","doi-asserted-by":"crossref","unstructured":"[3] Noboru Endou, Yasunari Shidama, and Keiichi Miyajima. Partial differentiation on normed linear spaces \u211bn. Formalized Mathematics, 15(2):65\u201372, 2007. doi:10.2478\/v10037-007-0008-5.","DOI":"10.2478\/v10037-007-0008-5"},{"key":"2026042801401829038_j_forma-2022-0012_ref_004","unstructured":"[4] Miyadera Isao. Functional Analysis. Riko-Gaku-Sya, 1972."},{"key":"2026042801401829038_j_forma-2022-0012_ref_005","doi-asserted-by":"crossref","unstructured":"[5] Kazuhisa Nakasho and Yuichi Futa. Inverse function theorem. Part I. Formalized Mathematics, 29(1):9\u201319, 2021. doi:10.2478\/forma-2021-0002.","DOI":"10.2478\/forma-2021-0002"},{"key":"2026042801401829038_j_forma-2022-0012_ref_006","doi-asserted-by":"crossref","unstructured":"[6] Kazuhisa Nakasho and Yasunari Shidama. Implicit function theorem. Part II. Formalized Mathematics, 27(2):117\u2013131, 2019. doi:10.2478\/forma-2019-0013.","DOI":"10.2478\/forma-2019-0013"},{"key":"2026042801401829038_j_forma-2022-0012_ref_007","doi-asserted-by":"crossref","unstructured":"[7] Kazuhisa Nakasho, Yuichi Futa, and Yasunari Shidama. Implicit function theorem. Part I. Formalized Mathematics, 25(4):269\u2013281, 2017. doi:10.1515\/forma-2017-0026.","DOI":"10.1515\/forma-2017-0026"},{"key":"2026042801401829038_j_forma-2022-0012_ref_008","doi-asserted-by":"crossref","unstructured":"[8] Kazuhisa Nakasho, Hiroyuki Okazaki, and Yasunari Shidama. Real vector space and related notions. Formalized Mathematics, 29(3):117\u2013127, 2021. doi:10.2478\/forma-2021-0012.","DOI":"10.2478\/forma-2021-0012"},{"key":"2026042801401829038_j_forma-2022-0012_ref_009","doi-asserted-by":"crossref","unstructured":"[9] Hiroyuki Okazaki, Noboru Endou, and Yasunari Shidama. Cartesian products of family of real linear spaces. Formalized Mathematics, 19(1):51\u201359, 2011. doi:10.2478\/v10037-011-0009-2.","DOI":"10.2478\/v10037-011-0009-2"},{"key":"2026042801401829038_j_forma-2022-0012_ref_010","unstructured":"[10] Laurent Schwartz. Th\u00e9orie des ensembles et topologie, tome 1. Analyse. Hermann, 1997."},{"key":"2026042801401829038_j_forma-2022-0012_ref_011","unstructured":"[11] Laurent Schwartz. Calcul diff\u00e9rentiel, tome 2. Analyse. Hermann, 1997."},{"key":"2026042801401829038_j_forma-2022-0012_ref_012","unstructured":"[12] K\u00f4saku Yosida. Functional Analysis. Springer, 1980."}],"container-title":["Formalized Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/reference-global.com\/pdf\/10.2478\/forma-2022-0012","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T13:39:52Z","timestamp":1777383592000},"score":1,"resource":{"primary":{"URL":"https:\/\/reference-global.com\/article\/10.2478\/forma-2022-0012"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,1]]},"references-count":12,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,12,30]]},"published-print":{"date-parts":[[2022,10,1]]}},"alternative-id":["10.2478\/forma-2022-0012"],"URL":"https:\/\/doi.org\/10.2478\/forma-2022-0012","relation":{},"ISSN":["1898-9934"],"issn-type":[{"value":"1898-9934","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,1]]}}}