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1
Content available remote Non-square points of Orlicz-Lorentz function spaces
EN
In this paper, criteria for non-square points in Orlicz-Lorentz function spaces Λφ,ω endowed with the Luxemburg norm are given. The widest possible classes of convex Orlicz functions and weight functions are admitted. In consequence, criteria for non-square points in Orlicz spaces Lφ, which generalize the already known results, are presented.
EN
Criteria in order that a Musielak-Orlicz function space Lφ as well as Musielak-Orlicz sequence space lφ contains an asymptotically isometric copy of c0 are given. These results extend some results of [Y.A. Cui, H. Hudzik, G. Lewicki, Order asymptotically isometric copies of c0 in the subspaces of order continuous elements in Orlicz spaces, Journal of Convex Analysis 21 (2014)] to Musielak-Orlicz spaces.
3
Content available remote K-extreme point of generalized Orlicz sequence spaces with Luxemburg norm
EN
In this paper,we give necessary and sufficient conditions in order that a point u∈S(l(Φ)) 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.
EN
In this paper, we present criteria for local uniform rotundity and weak local uniform rotundity in Musielak-Orlicz sequence spaces equipped with the Luxemburg norm.
5
Content available remote Orlicz-Bochner sequence spaces that have the uniform [lambda]-property
EN
Necessary and sufficient conditions in order that Orlicz-Bochner sequence spaces equipped with Luxemburg norm have the uniform [lambda] property are given.
7
Content available remote Continuity of the metric projection in Orlicz space
EN
Let (f(n)) be a sequence of functions converging in norm to f in some rotund Orlicz function or se-quence space endowed with the Luxemburg norm or the Orlicz norm, and let (C(n)) be a sequence of convex sets satisfying some condition and tending in suitable way to a ser C. Then the best norm approximation of f(n) with respect to C(n) converges in norm to the best approximation of f with respect to C.
8
Content available remote Haar system as a Schauder basis in Lp(x,y),q(y) (I)
EN
In this paper we define Lp(x,y),q(y) (I). We investigate some condition of this space.
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