A construction of convex functions (Q2435914)

In this paper, the author describes how to construct convex functions on infinite-dimensional spaces and then applies this construction to give an illustration to a theorem of \textit{J. M. Borwein} and \textit{M. Fabian} [Can. J. Math. 45, No. 6, 1121--1134 (1993; Zbl 0793.46021)] on the existence of Gâteau differentiability points that are not Fréchet differentiability points. More precisely, the author constructs on \(l_p\), \(p\geq1\), a convex continuous function which is everywhere compactly differentiable and is not Fréchet differentiable at zero.