<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We study mappings f : (a,b) → Y with finite dilation having Lebesgue integrable majorant, where Y is a real normed vector space. We construct Lipschitz mapping f : (a,b) → Y, dim Y = ∞ , which is nowhere differentiable but its graph has everywhere trivial contingent. We show that if the contingent of the graph of a mapping with finite dilation is a nontrivial space, then f is almost everywhere differentiable.</p></abstract>

We study mappings f : (a,b) → Y with finite dilation having Lebesgue integrable majorant, where Y is a real normed vector space. We construct Lipschitz mapping f : (a,b) → Y, dim Y = ∞ , which is nowhere differentiable but its graph has everywhere trivial contingent. We show that if the contingent of the graph of a mapping with finite dilation is a nontrivial space, then f is almost everywhere differentiable.

On differentiability of mappings with finite dilation

Institute of Mathematics Pomeranian University in Słupsk ul. Arciszewskiego 22d PL-76-200 Słupsk POLAND

Tatra Mountains Mathematical Publications

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{"article-title":"On differentiability of mappings with finite dilation"}

We study mappings f : (a,b) → Y with finite dilation having Lebesgue integrable majorant, where Y is a real normed vector space. We construct Lipschitz mapping...

On differentiability of mappings with finite dilation

Published Online: Sep 25, 2015

Page range: 133 - 141

Received: Oct 29, 2014

DOI: https://doi.org/10.1515/tmmp-2015-0010

© 2015

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.