Geodesic
On some equivalent geometric properties in the Besicovitch-Orlicz space of almost periodic functions with Luxemburg norm
Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 1, pp. 25-35.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 42A75, 46B20
Keywords: locally uniform convexity; strict convexity; $H$-property; Besicovitch-Orlicz space; almost periodic functions 
@article{CMUC_2010__51_1_a3,
     author = {Bedouhene, Fazia and Morsli, Mohamed and Smaali, Mannal},
     title = {On some equivalent geometric properties in the {Besicovitch-Orlicz} space of almost periodic functions with {Luxemburg} norm},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {25--35},
     publisher = {mathdoc},
     volume = {51},
     number = {1},
     year = {2010},
     mrnumber = {2666078},
     zbl = {1224.46018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2010__51_1_a3/}
}
TY  - JOUR
AU  - Bedouhene, Fazia
AU  - Morsli, Mohamed
AU  - Smaali, Mannal
TI  - On some equivalent geometric properties in the Besicovitch-Orlicz space of almost periodic functions with Luxemburg norm
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2010
SP  - 25
EP  - 35
VL  - 51
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2010__51_1_a3/
LA  - en
ID  - CMUC_2010__51_1_a3
ER  - 
%0 Journal Article
%A Bedouhene, Fazia
%A Morsli, Mohamed
%A Smaali, Mannal
%T On some equivalent geometric properties in the Besicovitch-Orlicz space of almost periodic functions with Luxemburg norm
%J Commentationes Mathematicae Universitatis Carolinae
%D 2010
%P 25-35
%V 51
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2010__51_1_a3/
%G en
%F CMUC_2010__51_1_a3
Bedouhene, Fazia; Morsli, Mohamed; Smaali, Mannal. On some equivalent geometric properties in the Besicovitch-Orlicz space of almost periodic functions with Luxemburg norm. Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 1, pp. 25-35. http://geodesic.mathdoc.fr/item/CMUC_2010__51_1_a3/