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Sibirskii Matematicheskii Zhurnal, 2009, Volume 50, Number 2, Pages 405–414 (Mi smj1968)  
On some properties of Lipschitz mappings of the real line into a normed space

S. P. Ponomarev, M. Turowska

Institute of Mathematics, Pomeranian Academy in Słupsk, Słupsk, Poland
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Abstract: We prove that for each normed space $Y$ of infinite dimension and each porous set $E\subset\mathbb R$ there exists a Lipschitz mapping $f\colon\mathbb R\to Y$ such that the graph of $f$ has a tangent at each of its points and f is not differentiable at any point of $E$. In this article we continue our research in [1] on contingents.
Keywords: normed space, contingent (tangent cone), Lipschitz mapping, differentiability, Steklov's regularization, porous set.
Received: 02.08.2007
Revised: 11.05.2008
English version:
Siberian Mathematical Journal, 2009, Volume 50, Issue 2, Pages 322–329
DOI: https://doi.org/10.1007/s11202-009-0037-0
Bibliographic databases:
UDC: 517.98.22
Language: Russian
Citation: S. P. Ponomarev, M. Turowska, “On some properties of Lipschitz mappings of the real line into a normed space”, Sibirsk. Mat. Zh., 50:2 (2009), 405–414; Siberian Math. J., 50:2 (2009), 322–329
Citation in format AMSBIB
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    		Сибирский математический журнал Siberian Mathematical Journal
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