On some equivalent geometric properties in the Besicovitch-Orlicz space of almost periodic functions with Luxemburg norm

Fazia Bedouhene; Mohamed Morsli; Mannal Smaali

Displaying similar documents to “On some equivalent geometric properties in the Besicovitch-Orlicz space of almost periodic functions with Luxemburg norm”

On some convexity properties in the Besicovitch-Musielak-Orlicz space of almost periodic functions with Luxemburg norm

Fazia Bedouhene, Amina Daoui, Hocine Kourat (2012)

Commentationes Mathematicae Universitatis Carolinae

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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 $({\tilde{B}}^{ϕ} a . p .)$ endowed with the Luxemburg norm.

Characterization of the strict convexity of the Besicovitch-Musielak-Orlicz space of almost periodic functions

Mohamed Morsli, Mannal Smaali (2007)

Commentationes Mathematicae Universitatis Carolinae

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We introduce the new class of Besicovitch-Musielak-Orlicz almost periodic functions and consider its strict convexity with respect to the Luxemburg norm.

Duality properties and Riesz representation theorem in Besicovitch-Musielak-Orlicz space of almost periodic functions

A. Daoui, Mohamed Morsli, M. Smaali (2012)

Commentationes Mathematicae Universitatis Carolinae

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This paper is an extension of the work done in [Morsli M., Bedouhene F., Boulahia F., Duality properties and Riesz representation theorem in the Besicovitch-Orlicz space of almost periodic functions, Comment. Math. Univ. Carolin. 43 (2002), no. 1, 103--117] to the Besicovitch-Musielak-Orlicz space of almost periodic functions. Necessary and sufficient conditions for the reflexivity of this space are given. A Riesz type ``duality representation theorem'' is also stated.