In this paper,we give necessary and sufficient conditions in order that a point is a k-extreme point in generalized Orlicz sequence spaces equipped with the Luxemburg norm, combing the methods used in classical Orlicz spaces and new methods introduced especially for generalized ones. The results indicate the difference between the classical Orlicz spaces and generalized Orlicz spaces.
We give a criterion of smoothness of Orlicz sequence spaces with Orlicz norm.
A criterion for strongly exposed points of the unit ball in Musielak-Orlicz sequence spaces equipped with Orlicz norm is given.
We discuss k-rotundity, weak k-rotundity, C-k-rotundity, weak C-k-rotundity, k-nearly uniform convexity, k-β property, C-I property, C-II property, C-III property and nearly uniform convexity both pointwise and global in Orlicz function spaces equipped with Luxemburg norm. Applications to continuity for the metric projection at a given point are given in Orlicz function spaces with Luxemburg norm.
Necessary and sufficient conditions are given for Orlicz sequence spaces equipped with the Orlicz norm to be uniformly rotund in a weakly compact set of directions, using only conditions on the generating function of the space.
We show that in Orlicz spaces equipped with Luxemburg norm and Orlicz norm, the RNP, CCP, PCP and CPCP are equivalent.
Page 1