On uniform convexity and modular approximation in the Weyl-Orlicz spaces

Czasopismo : Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
Tytuł artykułu : On uniform convexity and modular approximation in the Weyl-Orlicz spaces

Autorzy :
Anioł, G.
Faculty of Mathematics and Computer Science Adam Mickiewicz University, Jana Matejki 48/49, 60-769 Poznań, Poland, ganiol@amu.edu.pl,
Banaś, J.
Department of Mathematics Technical University of Rzeszów W.Pola 2, 35-959 Rzeszów, piejko@prz.rzeszow.pl,
Bedouhene, F.
Depart.Maths.Faculté Sciences, Université de Tizi-Ouzou, Algérie, morsli@ifrance.com,
Abstrakty : Uniform convexity is well characterized in Orlicz spaces for both the Luxemburg and Orlicz norms [2], [3], [4] and in Besicovitch-Orlicz spaces of almost periodic functions for the Luxemburg norm [7]. The existence problem of the projection operator on closed convex subsets was considered in [5] in the case of Orlicz spaces, and in [8] in the case of Besicovitch-Orlicz space of almost periodic functions. In this paper we characterize the uniform convexity property in the Weyl-Orlicz spaces of almost periodic functions (W^a.p.) under the Luxemburg norm. Next this result is used to state the existence of the projection operator on complete convex subsets of W^a.p.

Słowa kluczowe : Weyl-Orlicz space, almost periodic functions, uniform convexity, modular approximation,
Wydawnictwo : Polskie Towarzystwo Matematyczne
Rocznik : 2001
Numer : [Z] 41
Strony : 25 – 39
Bibliografia :
DOI :
Cytuj : Anioł, G. ,Banaś, J. ,Bedouhene, F. , On uniform convexity and modular approximation in the Weyl-Orlicz spaces. Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae [Z] 41/2001
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