A construction of convex functions |
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Authors: | T. Konderla |
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Affiliation: | 1. Mathematical Institute, Silesian University in Opava, Opava, Czech Republic
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Abstract: | We describe a construction of convex functions on infinite-dimensional spaces and apply this construction to give an illustration to a theorem of Borwein-Fabian from [1]. Namely, we give a simple explicit example of a continuous convex function on l p , p ≥ 1, which is everywhere compactly differentiable, but not Fréchet differentiable at zero. |
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