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/