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Main results include the Lipschitz continuity of partial derivatives, the representation of the total derivative in terms of partial derivatives, and the continuous differentiability of Lipschitzian bilinear operators on open subsets of the product space.<\/jats:p>","DOI":"10.2478\/forma-2024-0013","type":"journal-article","created":{"date-parts":[[2025,1,3]],"date-time":"2025-01-03T14:07:48Z","timestamp":1735913268000},"page":"165-172","source":"Crossref","is-referenced-by-count":1,"title":["Differentiability Properties of Lipschitzian Bilinear Operators 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":"2026042801431968324_j_forma-2024-0013_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":"2026042801431968324_j_forma-2024-0013_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":"2026042801431968324_j_forma-2024-0013_ref_003","unstructured":"Nelson Dunford and Jacob T. Schwartz. Linear operators I. 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