On the k-convexity of the Besicovitch-Orlicz space of almost periodic functions with the Orlicz norm
Fazia Bedouhene ; Mohamed Morsli
Colloquium Mathematicae, Tome 107 (2007), p. 107-118 / Harvested from The Polish Digital Mathematics Library
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Boulahia and the present authors introduced the Orlicz norm in the class Bϕ-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 Bϕ-a.p. with respect to the Orlicz norm; we give necessary and sufficient conditions in terms of strict convexity and reflexivity.

Publié le : 2007-01-01
EUDML-ID : urn:eudml:doc:284001 
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     title = {On the k-convexity of the Besicovitch-Orlicz space of almost periodic functions with the Orlicz norm},
     journal = {Colloquium Mathematicae},
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     year = {2007},
     pages = {107-118},
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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 Mathematicae, Tome 107 (2007) pp. 107-118. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm109-1-9/