Characterization of the k-convexity property in the Besicovitch-Orlicz space of almost periodic functions

• Autorzy: Bedouhene F. , Morsli M.
• Języki publikacji: EN

Abstrakty

EN

In the present paper, we give criteria for the k-convexity of the Besicovitch-Orlicz space of almost periodic functions. Namely,it is shown that k-convexity is equivalent to strict convexity and reflexivity of this space in the case of Luxemburg norm.

Słowa kluczowe

EN

modular function space; nonlinear integral operator; Cauchy conservative family of operators

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2005
• Tom: Vol. 45, [Z] 1
• Strony: 13--23
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Bedouhene F.

• Department of Mathematics. Faculty of Sciences.University of Tizi-Ouzou Oued-Aissi, Algeria

autor

Morsli M.

• Department of Mathematics. Faculty of Sciences.University of Tizi-Ouzou Oued-Aissi, Algeria

Bibliografia

• [1] S. Chen, Geometry of Orlicz spaces, Dissertationes Math. 356, 1996.
• [2] T. R. Hillmann, Besicovitch-Orlicz spaces of almost periodic functions, Real and Stochastic Analysis, Wiley Ser. in Probability and Math Statist. Wiley, New-York (1986), 119-167.
• [3] M. A. Krasnoselskii and Y. B. Rutickii, Convex functions and Orlicz spaces, P. Noodhoff Ltd.,Groningen 1961.
• [4] M. Morsli, On some convexity properties of the Besicovitch-Orlicz space of almost periodic functions, Comment.Math. 34 (1994), 137-152.
• [5] M. Morsli, Espace de Besicovitch Orlicz de fonctions presque periodiques. Structure generale et geometrie, These de Doctorat, 1996.
• [6] M. Morsli, On modular approximation property in the Besicovitch-Orlicz space of almost periodic functions, Comment. Math. Univ. Carolinae 38(3) (1997), 485-496.
• [7] J. Musielak and W. Orlicz, On modular space, Studia Math. 18 (1959), 49-65.
• [8] M. M. Rao and Z. D. Ren, Theory of Orlicz spaces, Marcel Dekker, Inc. New-York 1991.