Further properties of Stepanov--Orlicz  almost periodic functions

Yousra Djabri; Fazia Bedouhene; Fatiha Boulahia

Displaying similar documents to “Further properties of Stepanov--Orlicz almost periodic functions”

Extreme points of the Besicovitch--Orlicz space of almost periodic functions equipped with the Luxemburg norm

Slimane Hassaine, Fatiha Boulahia (2021)

Commentationes Mathematicae Universitatis Carolinae

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We investigate which points in the unit sphere of the Besicovitch--Orlicz space of almost periodic functions, equipped with the Luxemburg norm, are extreme points. Sufficient conditions for the strict convexity of this space are also given.

On the uniform convexity of the Besicovitch-Orlicz space of almost periodic functions with Orlicz norm

Mohamed Morsli, Fazia Bedouhene (2005)

Colloquium Mathematicae

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In [5], we characterized the uniform convexity with respect to the Luxemburg norm of the Besicovitch-Orlicz space of almost periodic functions. Here we give an analogous result when this space is endowed with the Orlicz norm.

Uniform non-squareness and property $(β)$ of Besicovitch-Orlicz spaces of almost periodic functions with Orlicz norm

Fatiha Boulahia, Mohamed Morsli (2010)

Commentationes Mathematicae Universitatis Carolinae

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We characterize the uniform non-squareness and the property $(β)$ of Besicovitch-Orlicz spaces of almost periodic functions equipped with Orlicz norm.

On the strict convexity of the Besicovitch-Orlicz space of almost periodic functions with Orlicz norm.

Mohamed Morsli, Fazia Bedouhene (2003)

Revista Matemática Complutense

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The problem of strict convexity of the Besicovitch-Orlicz space of almost periodic functions is considered here in connection with the Orlicz norm. We give necessary and sufficient conditions in terms of the function f generating the space.

Generalized almost periodic functions

J. W. McCoy (1970)

Colloquium Mathematicae

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On nth-order differential operators with Bohr-Neugebauer type property.

Aribindi Satyanarayan Rao (1987)

International Journal of Mathematics and Mathematical Sciences

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On the Stepanov almost periodic solution of a second-order infinitesimal generator differential equation.

Rao, Aribindi Satyanarayan (1991)

International Journal of Mathematics and Mathematical Sciences

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Almost periodic solutions to second order neutral differential equations.

Corduneanu, C. (2005)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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On the k-convexity of the Besicovitch-Orlicz space of almost periodic functions with the Orlicz norm

Fazia Bedouhene, Mohamed Morsli (2007)

Colloquium Mathematicae

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Boulahia and the present authors introduced the Orlicz norm in the class $B^{ϕ}$ -a.p. of Besicovitch-Orlicz almost periodic functions and gave several formulas for it; they also characterized the reflexivity of this space [Comment. Math. Univ. Carolin. 43 (2002)]. In the present paper, we consider the problem of k-convexity of $B^{ϕ}$ -a.p. with respect to the Orlicz norm; we give necessary and sufficient conditions in terms of strict convexity and reflexivity.

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

Mohamed Morsli, Fazia Bedouhene, Fatiha Boulahia (2002)

Commentationes Mathematicae Universitatis Carolinae

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In [6], the classical Riesz representation theorem is extended to the class of Besicovitch space of almost periodic functions $B^{q}$ a.p., $q \in] 1, + \infty [$ . It is also shown that this space is reflexive. We shall consider here such results in the context of Orlicz spaces, namely in the class of Besicovitch-Orlicz space of almost periodic functions $B^{φ}$ a.p., where $φ$ is an Orlicz function.