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
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
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
Affiliations des auteurs :
Fazia Bedouhene 1 ; Mohamed Morsli 2
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author = {Fazia Bedouhene and Mohamed Morsli},
title = {On the $k$-convexity of the {Besicovitch{\textendash}Orlicz} space
of almost periodic functions
with the {Orlicz} norm},
journal = {Colloquium Mathematicum},
pages = {107--118},
publisher = {mathdoc},
volume = {109},
number = {1},
year = {2007},
doi = {10.4064/cm109-1-9},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm109-1-9/}
}
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%0 Journal Article %A Fazia Bedouhene %A Mohamed Morsli %T On the $k$-convexity of the Besicovitch–Orlicz space of almost periodic functions with the Orlicz norm %J Colloquium Mathematicum %D 2007 %P 107-118 %V 109 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/cm109-1-9/ %R 10.4064/cm109-1-9 %G en %F 10_4064_cm109_1_9
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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