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3 Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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Characterization of the k-convexity property in the Besicovitch-Orlicz space of almost periodic functions

Bedouhene F., Morsli M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2005

Vol. 45, [Z] 1

13--23

In the present paper, we give criteria for the k-convexity of the Besicovitch-Orlicz space of almost periodic functions. Namely,it is shown that k-convexity is equivalent to strict convexity and reflexivity of this space in the case of Luxemburg norm.

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

Bedouhene F., Morsli M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2001

[Z] 41

25-39

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.

On strict convexity of the Weyl-Orlicz space of almost periodic functions

Bedouhene F., Morsli M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2000

[Z] 40

33-47

Abstract. In [2], T.R. Hillmann investigated some structural and topo-logical properties of the Besicovitch-Orlicz space (and others like as the Stepanoff and Weyl-Orlicz spaces) and his subspaces of almost periodic functions. In [3], we characterized the strict and uniform convexity of this space. In this paper, the strict convexity property is characterized in the Weyl-Orlicz space of almost periodic functions