Geodesic
On Gâteaux Differentiability of Convex Functions in WCG Spaces
Canadian mathematical bulletin, Tome 48 (2005) no. 3, pp. 455-459

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DOI

It is shown, using the Borwein–Preiss variational principle that for every continuous convex function $f$ on a weakly compactly generated space $X$ , every ${{x}_{0}}\in X$ and every weakly compact convex symmetric set $K$ such that $\overline{\text{span}}K=X$ , there is a point of Gâteaux differentiability of $f$ in ${{x}_{0}}+K$ . This extends a Klee's result for separable spaces.
DOI : 10.4153/CMB-2005-042-7
Mots-clés : 46B20, Gâteaux smoothness, Borwein–Preiss variational principle, weakly compactly generated spaces 
Rychtář, Jan. On Gâteaux Differentiability of Convex Functions in WCG Spaces. Canadian mathematical bulletin, Tome 48 (2005) no. 3, pp. 455-459. doi: 10.4153/CMB-2005-042-7
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     title = {On {G\^ateaux} {Differentiability} of {Convex} {Functions} in {WCG} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {455--459},
     year = {2005},
     volume = {48},
     number = {3},
     doi = {10.4153/CMB-2005-042-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-042-7/}
}
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