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