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

100%

Bedouhene F. , Morsli M.

Commentationes Mathematicae

2005

tom 45

nr 1

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 the k-convexity of the Besicovitch-Orlicz space of almost periodic functions with the Orlicz norm

100%

Bedouhene F. , Morsli M.

Colloquium Mathematicum

2007

tom 109

nr 1

107-118

Boulahia and the present authors introduced the Orlicz norm in the class $B^{ϕ}$-a.p. of Besicovitch-Orlicz almost periodic functions and gave several formulas for it; they also characterized the reflexivity of this space [Comment. Math. Univ. Carolin. 43 (2002)]. In the present paper, we consider the problem of k-convexity of $B^{ϕ}$-a.p. with respect to the Orlicz norm; we give necessary and sufficient conditions in terms of strict convexity and reflexivity.

On the uniform convexity of the Besicovitch-Orlicz space of almost periodic functions with Orlicz norm

100%

Morsli M. , Bedouhene F.

tom 102

nr 1

97-111

In [5], we characterized the uniform convexity with respect to the Luxemburg norm of the Besicovitch-Orlicz space of almost periodic functions. Here we give an analogous result when this space is endowed with the Orlicz norm.