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# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## On the $k$-convexity of the Besicovitch–Orlicz space of almost periodic functions with the Orlicz norm

### Tom 109 / 2007

Colloquium Mathematicum 109 (2007), 107-118 MSC: 46B20, 42A75. DOI: 10.4064/cm109-1-9

#### Streszczenie

Boulahia and the present authors introduced the Orlicz norm in the class $B^{\phi }$-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 $B^{\phi }$-a.p. with respect to the Orlicz norm; we give necessary and sufficient conditions in terms of strict convexity and reflexivity.

#### Autorzy

• Fazia BedouheneDepartment of Mathematics
Faculty of Sciences
University of Tizi-Ouzou, Algeria
e-mail
• Mohamed MorsliDepartment of Mathematics
Faculty of Sciences
University of Tizi-Ouzou
Algeria
e-mail

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