Geodesic
A Construction of Convex Functions
Matematičeskie zametki, Tome 91 (2012) no. 1, pp. 74-78

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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 $l_p$, $p\ge 1$, which is everywhere compactly differentiable, but not Fréchet differentiable at zero.
Keywords: topological vector space, normed space, convex function, Fréchet differentiability, Gâteaux differentiability, compact differentiability. 
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     author = {T. Konderla},
     title = {A {Construction} of {Convex} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {74--78},
     publisher = {mathdoc},
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     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_1_a6/}
}
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T. Konderla. A Construction of Convex Functions. Matematičeskie zametki, Tome 91 (2012) no. 1, pp. 74-78. http://geodesic.mathdoc.fr/item/MZM_2012_91_1_a6/