Uniform Gateaux differentiability and weak uniform rotundity of Musielak-Orlicz function spaces. (Q1428632)

The authors present a simple proof dealing with criteria for uniform Gâteaux differentiability of Musielak-Orlicz spaces equipped with the Luxemburg norm and weak uniform rotundity of the subspaces of order continuous elements of Musielak-Orlicz spaces endowed with the Orlicz norm. The criteria are even new in the case of Orlicz spaces. The authors indicate that the criteria for the Orlicz norm are different from those for the Luxemburg norm. The topic of the paper is related to fixed point theory.