Fazia Bedouhene, Amina Daoui, Hocine Kourat
On some convexity properties in the Besicovitch-Musielak-Orlicz space of almost periodic functions with Luxemburg norm

Comment.Math.Univ.Carolin. 53,4 (2012) 535-547.

Abstract: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.

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
AMS Subject Classification: 46B20 42A75

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