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oai:kanazawa-u.repo.nii.ac.jp:00010516 2024-06-20T06:08:06Z 934:935:937

On the critical case of Okamoto's continuous non-differentiable functions Kobayashi, Kenta 15953 60432902 In a recent paper in this Proceedings, H. Okamoto presented a parameterized family of continuous functions which contains Bourbaki's and Perkins's nowhere differentiable functions as well as the Cantor-Lebesgue singular function. He showed that the function changes it's differentiability from 'differentiable almost everywhere' to 'non-differentiable almost everywhere' at a certain parameter value. However, differentiability of the function at the critical parameter value remained unknown. For this problem, we prove that the function is non-differentiable almost everywhere at the critical case. © 2009 The Japan Academy. journal article 日本学士院 = Japan Academy 2009-01-01 VoR application/pdf Proceedings of the Japan Academy Series A: Mathematical Sciences 8 85 101 104 AA00785474 0386-2194 https://kanazawa-u.repo.nii.ac.jp/record/10516/files/SC-PR-KOBAYASHI-K-101.pdf http://hdl.handle.net/2297/37862 https://kanazawa-u.repo.nii.ac.jp/records/10516 eng 10.3792/pjaa.85.101 http://www.japan-acad.go.jp/ http://projecteuclid.org/ Copyright © The Japan Academy