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Tytuł artykułu

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

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the present paper, we give criteria for the existence of extreme points of the Besicovitch-Orlicz space of almost periodic functions equipped with Orlicz norm. Some properties of the set of attainable points of the Amemiya norm in this space are also discussed.
Rocznik
Strony
629--648
Opis fizyczny
BIbliogr. 21 poz.
Twórcy
  • University A. Mira of Bejaia Laboratory of Applied Mathematics Department of Mathematics Faculty of Exact Sciences Targa Ouzemour, 06000 Bejaia, Algeria
  • University of Mouloud Mammeri, Tizi-Ouzou Department of Mathematics Faculty of Sciences Tizi-Ouzou BP No. 17, RP 15000, Algeria
  • University of Bejaia Laboratory of Applied Mathematics Algeria
Bibliografia
  • [1] F. Bedouhene, M. Morsli, M. Smaali, On some equivalent geometric properties in the Besicovitch-Orlicz space of almost periodic functions with Luxemburg norm, Commentat. Math. Univ. Carol. 51 (2010), no. 1, 25-35.
  • [2] A.S. Besicovitch, Almost Periodic Functions, Neudruck, New York: Dover Publications, 1955.
  • [3] F. Boulahia, M. Morsli, Uniform non-squareness and property (ß) of Besicovitch-Orlicz spaces of almost periodic functions with Orlicz norm, Comment. Math. Univ. Carol. 51 (2010), no. 3, 417-426.
  • [4] S. Chen, Geometry of Orlicz spaces, Dissertationes Math. 356 (1996).
  • [5] J. Diestel, Geometry of Banach Spaces: Selected Topics, Springer, 1975.
  • [6] Y. Djabri, F. Bedouhene, F. Boulahia, Further properties of Stepanov-Orlicz almost periodic functions, Comment. Math. Univ. Carol. 61 (2020), no. 3, 363-382.
  • [7] P. Foralewski, H. Hudzik, R. Płuciennik, Orlicz spaces without extreme points, J. Math. Anal. Appl. 361 (2010), no. 2, 506-519.
  • [8] S. Hassaine, F. Boulahia, Extreme points of the Besicovitch-Orlicz space of almost periodic functions equipped with the Luxemburg norm, Comment. Math. Univ. Carol. 62 (2021), no. 1, 67-79.
  • [9] T.R. Hillmann, Besicovitch-Orlicz spaces of almost periodic functions, Real and Stochas¬tic Analysis, Wiley Ser. Probab. Math. Stat., 119-167, 1986.
  • [10] K.S. Lau, On the Banach spaces of functions with bounded upper means, Pac. J. Appl. Math. 91 (1980), no. 1, 153-172.
  • [11] M. Morsli, On some convexity properties of the Besicovitch-Orlicz space of almost periodic functions, Comment. Math. 34 (1994), 137-152.
  • [12] M. Morsli, On modular approximation property in the Besicovitch-Orlicz space of almost periodic functions, Commentat. Math. Univ. Carolin. 38 (1997), no. 3, 485-496.
  • [13] M. Morsli, F. Bedouhene, On the strict convexity of the Besicovitch-Orlicz space of almost periodic functions with Orlicz norm, Rev. Mat. Complut. 16 (2003), no. 2, 399-415.
  • [14] M. Morsli, F. Bedouhene, On the uniform convexity of the Besicovitch-Orlicz space of almost periodic functions with Orlicz norm, Colloq. Math. 102 (2005), no. 1, 97-111.
  • [15] M. Morsli, F. Boulahia, Uniformly non-l1n Besicovitch-Orlicz space of almost periodic functions, Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 45 (2005), no. 1, 25-34.
  • [16] M. Morsli, F. Bedouhene, F. Boulahia, Duality properties and Riesz representation theorem in the Besicovitch-Orlicz space of almost periodic function, Comment. Math. Univ. Carol. 43 (2002), no. 1, 103-117.
  • [17] M. Morsli, M. Smaali, On the strict convexity of the Besicovitch-Musielak-Orlicz space of almost periodic functions, Commentat. Math. Unvi. Carol. 48 (2007), no. 3, 443-458.
  • [18] M.A. Picardello, Function spaces with bounded Lp means and their continuous functionals, Abstr. Appl. Anal. 2014 (2014), Article no. 609525.
  • [19] S. Shang, Y. Cui, Y. Fu, Extreme points and rotundity in Musielak-Orlicz-Bochner function spaces endowed with Orlicz norm, Abstr. Appl. Anal. 2010 (2010), Article no. 914183.
  • [20] W. Stepanoff, Einige Veral lgemeinerungen der fast periodischen Funktionen, Math. Ann. 95 (1926), no. 1, 473-498.
  • [21] M. Wisła, Geometric properties of Orlicz spaces equipped with p-Amemiya norms - results and open questions, Commentat. Math. 55 (2015), no. 2, 183-209.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-127515f1-2f05-406a-b529-78dc1f4788ea
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