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

Mohamed Morsli; Mannal Smaali

Displaying similar documents to “Characterization of the strict convexity of the Besicovitch-Musielak-Orlicz space of almost periodic functions”

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

Fazia Bedouhene, Mohamed Morsli, Mannal Smaali (2010)

Commentationes Mathematicae Universitatis Carolinae

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The paper is concerned with the characterization and comparison of some local geometric properties of the Besicovitch-Orlicz space of almost periodic functions. Namely, it is shown that local uniform convexity, $H$ -property and strict convexity are all equivalent. In our approach, we first prove some metric type properties for the modular function associated to our space. These are then used to prove our main equivalence result.

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.

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.

Notes on approximation in the Musielak-Orlicz spaces of vector multifunctions

Andrzej Kasperski (1994)

Commentationes Mathematicae Universitatis Carolinae

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We introduce the spaces $M_{Y, ϕ}^{1}$ , $M_{Y, ϕ}^{o, n}$ , ${\tilde{M}}_{Y, ϕ}^{o}$ and $M_{Y, 𝐝, ϕ}^{o}$ of multifunctions. We prove that the spaces $M_{Y, ϕ}^{1}$ and $M_{Y, 𝐝, ϕ}^{o}$ are complete. Also, we get some convergence theorems.