On modular approximation property in the Besicovitch-Orlicz space of almost periodic functions

Mohamed Morsli

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 3, page 485-496
  • ISSN: 0010-2628

Abstract

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We investigate some convergence questions in the class of Besicovitch-Orlicz spaces of vector valued functions. Next, the existence problem of the projection operator on closed convex subsets is considered in the class of almost periodic functions. This problem was considered in [5], in the case of an Orlicz space. The approximation property obtained in both cases are of the same kind. However, the arguments which are used in the proofs are different.

How to cite

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Morsli, Mohamed. "On modular approximation property in the Besicovitch-Orlicz space of almost periodic functions." Commentationes Mathematicae Universitatis Carolinae 38.3 (1997): 485-496. <http://eudml.org/doc/248058>.

@article{Morsli1997,
abstract = {We investigate some convergence questions in the class of Besicovitch-Orlicz spaces of vector valued functions. Next, the existence problem of the projection operator on closed convex subsets is considered in the class of almost periodic functions. This problem was considered in [5], in the case of an Orlicz space. The approximation property obtained in both cases are of the same kind. However, the arguments which are used in the proofs are different.},
author = {Morsli, Mohamed},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {modular approximation; Besicovitch-Orlicz space; almost periodic functions; modular approximation; Besicovitch-Orlicz space; almost periodic functions},
language = {eng},
number = {3},
pages = {485-496},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On modular approximation property in the Besicovitch-Orlicz space of almost periodic functions},
url = {http://eudml.org/doc/248058},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Morsli, Mohamed
TI - On modular approximation property in the Besicovitch-Orlicz space of almost periodic functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 3
SP - 485
EP - 496
AB - We investigate some convergence questions in the class of Besicovitch-Orlicz spaces of vector valued functions. Next, the existence problem of the projection operator on closed convex subsets is considered in the class of almost periodic functions. This problem was considered in [5], in the case of an Orlicz space. The approximation property obtained in both cases are of the same kind. However, the arguments which are used in the proofs are different.
LA - eng
KW - modular approximation; Besicovitch-Orlicz space; almost periodic functions; modular approximation; Besicovitch-Orlicz space; almost periodic functions
UR - http://eudml.org/doc/248058
ER -

References

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  1. Hillmann T.R., Besicovitch-Orlicz spaces of almost periodic functions, Real and Stochastic Analysis, Wiley, 1986, pp.119-167. Zbl0656.46020MR0856581
  2. Hudzik H., An estimation of the modulus of convexity in a class of Orlicz spaces, Math. Japonica 32 2 (1987), 227-237. (1987) Zbl0637.46031MR0895543
  3. Hudzik H., Convexity in Musielak-Orlicz spaces, Hokkaido Math. J. 14 (1985), 85-96. (1985) Zbl0579.46023MR0781829
  4. Kaminska A., On uniform convexity of Orlicz space, Indag. Math. 44.1 (1982), 27-36. (1982) MR0653453
  5. Khamsi M., Kozlowski W., Shutao C., Some geometrical properties and fixed point theorems in Orlicz spaces, J. of Math. and Appl., vol 155, no. 2, March 1, 1991. Zbl0752.46011MR1097290
  6. Morsli M., Some convexity properties of the Besicovitch-Orlicz space of almost periodic functions, Comment. Math. 34 (1994), 137-152. (1994) Zbl0839.46012MR1325081
  7. Morsli M., On uniform convexity of Besicovitch-Orlicz space of almost periodic functions, Functiones et Approximatio 22 (1993), 95-106. (1993) MR1304363
  8. Musielak J., Orlicz W., On modular space, Studia Math. 18 (1959), 49-65. (1959) MR0101487
  9. Nakano H., Topology and Linear Topological Spaces, Tokyo, 1951. MR0046560

Citations in EuDML Documents

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  1. Fazia Bedouhene, Mohamed Morsli, Mannal Smaali, On some equivalent geometric properties in the Besicovitch-Orlicz space of almost periodic functions with Luxemburg norm
  2. Mohamed Morsli, Fazia Bedouhene, Fatiha Boulahia, Duality properties and Riesz representation theorem in the Besicovitch-Orlicz space of almost periodic functions
  3. Slimane Hassaine, Fatiha Boulahia, Extreme points of the Besicovitch--Orlicz space of almost periodic functions equipped with the Luxemburg norm

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