It is proved that no convex and Fréchet differentiable function on c0(w1), whose derivative is locally uniformly continuous, attains its minimum at a unique point.
@article{urn:eudml:doc:40284, title = {On convex functions in c0(w1).}, journal = {Collectanea Mathematica}, volume = {47}, year = {1996}, pages = {111-115}, zbl = {0859.46027}, mrnumber = {MR1402064}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40284} }
Hájek, Petr. On convex functions in c0(w1).. Collectanea Mathematica, Tome 47 (1996) pp. 111-115. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40284/