Geodesic
On the $k$-convexity of the Besicovitch–Orlicz space of almost periodic functions with the Orlicz norm
Fazia Bedouhene 1   ; Mohamed Morsli 2
1 Department of Mathematics Faculty of Sciences University of Tizi-Ouzou, Algeria
2 Department of Mathematics Faculty of Sciences University of Tizi-Ouzou Algeria
Colloquium Mathematicum, Tome 109 (2007) no. 1, pp. 107-118 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm109-1-9
Keywords: boulahia present authors introduced orlicz norm class phi a besicovitch orlicz almost periodic functions gave several formulas characterized reflexivity space comment math univ carolin present paper consider problem k convexity phi a respect orlicz norm necessary sufficient conditions terms strict convexity reflexivity

Fazia Bedouhene  1   ; Mohamed Morsli  2

1 Department of Mathematics Faculty of Sciences University of Tizi-Ouzou, Algeria
2 Department of Mathematics Faculty of Sciences University of Tizi-Ouzou Algeria 
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 with the Orlicz norm
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Fazia Bedouhene; Mohamed Morsli. On the $k$-convexity of the Besicovitch–Orlicz space
 of almost periodic functions
 with the Orlicz norm. Colloquium Mathematicum, Tome 109 (2007) no. 1, pp. 107-118. doi: 10.4064/cm109-1-9

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