On the critical case of Okamoto's continuous non-differentiable functions
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説明
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.
収録刊行物
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- Proceedings of the Japan Academy Series A: Mathematical Sciences
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Proceedings of the Japan Academy Series A: Mathematical Sciences 85 (8), 101-104, 2009-01-01
日本学士院 = Japan Academy
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詳細情報 詳細情報について
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- CRID
- 1573105977481534976
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- NII論文ID
- 120005447707
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- NII書誌ID
- AA00785474
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- ISSN
- 03862194
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- Web Site
- http://hdl.handle.net/2297/37862
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- 本文言語コード
- en
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- データソース種別
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