Geodesic
On some convexity properties in the Besicovitch-Musielak-Orlicz space of almost periodic functions with Luxemburg norm
Commentationes Mathematicae Universitatis Carolinae, Tome 53 (2012) no. 4, pp. 535-547.

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In this article, it is shown that geometrical properties such as local uniform convexity, mid point local uniform convexity, H-property and uniform convexity in every direction are equivalent in the Besicovitch-Musielak-Orlicz space of almost periodic functions $(\widetilde{B}^{\varphi }a.p.)$ endowed with the Luxemburg norm.
Classification : 42A75, 46B20
Keywords: local uniform convexity; uniform convexity in every direction; mid point locally uniform; H-property; strict convexity; approximation; Besicovitch-Musielak-Orlicz space; almost periodic function 
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Bedouhene, Fazia; Daoui, Amina; Kourat, Hocine. On some convexity properties in the Besicovitch-Musielak-Orlicz space of almost periodic functions with Luxemburg norm. Commentationes Mathematicae Universitatis Carolinae, Tome 53 (2012) no. 4, pp. 535-547. http://geodesic.mathdoc.fr/item/CMUC_2012__53_4_a2/