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1
Content available remote Extreme points of the Besicovitch-Orlicz space of almost periodic functions equipped with Orlicz norm
Boulahia Fatiha, Hassaine Slimane
Opuscula Mathematica
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2021
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Vol. 41, no. 5
629--648
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.
2
Content available remote On the strict convexity of Besicovitch-Musielak-Orlicz spaces of almost periodic functions equipped with the Orlicz norm
Daoui A., Morsli M., Smaali M.
Commentationes Mathematicae
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2013
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Vol. 53, No. 2
101--111
EN
We characterize the strict convexity of Besicovitch-Musielak-Orlicz spaces of almost periodic functions, when it is equipped with the Orlicz norm. It is shown that this property is equivalent to the strict convexity of the Musielak-Orlicz function generating the space.
3
Content available remote A note on the primitive function of a Bohr almost periodic function
Stoiński S.
Commentationes Mathematicae
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2011
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Vol. 51, [Z] 1
77-80
EN
In this article we prove a sufficient condition for the primitive function of a uniformly almost periodic function to be Bohr almost periodic.
4
Content available remote On the quasi N-almost periodic functions
Stoiński S.
Commentationes Mathematicae
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2010
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Vol. 50, [Z] 1
61-67
EN
In this note we present the definition, examples and some properties of quasi N–almost periodic functions, i. e. certain almost periodic functions in the sense of Levitan.
5
Content available remote On the almost periodic functions in the sense of Levitan
Michałowicz A., Stoiński S.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2007
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Vol. 47, [Z] 2
149-159
EN
In this note we present some theorems on the superposition of an (NVp)-almost periodic (a.p. for short) function, a μ-a.p. function and an (Nμ)-a.p. function. Moreover, we prove a theorem on the bounded primary function of an (NS^p)-a.p. function. Finally, we prove that the inverse of a V_p-a.p. function is (NV_p)-a.p.
6
Content available remote Characterization of the uniform convexity of the Besicovitch-Musielak-Orlicz spaces of almost periodic functions
Morsli M., Smaali M.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2006
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Vol. 46, [Z] 2
215-231
EN
We introduce the new class of Besicovitch-Musielak-Orlicz spaces of almost periodic functions B'a.p..The uniform convexity of this space is characterized in terms of it’s generating functional [fi]
7
Content available remote Uniformly non-[formula] Besicovitch-Orlicz space of almost periodic functions
Morsli M., Boulahia F.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2005
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Vol. 45, [Z] 1
25--34
EN
We consider uniformly non-[formula] property of the Besicovitch-Orlicz space of almost periodic functions. It is shownthat this property is equivalent to the reflexivity of this space.
8
Content available remote A note on N-almost periodic functions and (NI)-almost periodic functions
Stoiński S.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2004
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Vol. 44, nr 2
199-204
EN
This paper presents some remarke on the N-almost periodic functions and the definitions and some properties of the (NI)-almost periodic functions, i.e. almost periodic functions in the sense of Levitan with its primary function.
9
Content available remote Critical points of almost periodic functions
Janeczko S., Zając M.
Bulletin of the Polish Academy of Sciences. Mathematics
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2003
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Vol. 51, no 1
107-120
EN
The spaces of almost periodic and quasi-periodic functions are considered. We show that the local critical point properties can continue along the domain with the relative density property, and vanishing of the appropriate derivatives is only a "virtual" property. The stable virtual critical points of quasi-periodic functions are classified and the density result for the virtual critical points of type A(k) is proved. The special construction of almost periodic functions with prescribed properties is provided and applied to construct an almost periodic function which nas no density property of the nondegenerate critical points, althougth all its derivatives are almost periodic functions.
10
Content available remote On some perturbations of some abstract differential equations
Diagana T., Nguerekata G. M.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2003
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[Z] 43(2)
201-206
EN
We are concerned with the existence of almost automorphic mild solutions to the perturbed abstract differential equations of the form x(t) = (A + B)x(t) (*), where A is a unbounded linear operator generator of a Co-group of bounded operators and B is a bounded linear operator acting in a Banach space X. Under suitable conditions we show that every bounded mild solution to (*) is almost automorphic. Meanwhile under a relatively compactness hypothesis of the range of a solution, we show that such a solution is also almost periodic.
11
Content available remote On uniform convexity and modular approximation in the Weyl-Orlicz spaces
Bedouhene F., Morsli M.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2001
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[Z] 41
25-39
EN
Uniform convexity is well characterized in Orlicz spaces for both the Luxemburg and Orlicz norms [2], [3], [4] and in Besicovitch-Orlicz spaces of almost periodic functions for the Luxemburg norm [7]. The existence problem of the projection operator on closed convex subsets was considered in [5] in the case of Orlicz spaces, and in [8] in the case of Besicovitch-Orlicz space of almost periodic functions. In this paper we characterize the uniform convexity property in the Weyl-Orlicz spaces of almost periodic functions (W^a.p.) under the Luxemburg norm. Next this result is used to state the existence of the projection operator on complete convex subsets of W^a.p.
12
Content available remote N- almost periodic in the sense of variation functions
Stoiński S.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2001
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[Z] 41
195-202
EN
In this paper we present the definitions and some theorems on (N,V) - almost periodic (a.p.) functions (N,S^p)-a.p. functions and (N,V_p)-a.p. functions. We prove that if f is an (N,S)-a.p. function and the indefinite integral F of f is bounded, them F is (N,V)-a.p.
13
Content available remote On the derivative of a Bohr's almost periodic function
Stoiński S.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2000
|
[Z] 40
174-180
EN
In this note we present some theorems on the connection between a continuity of the derivative f' of a Bohr's almost periodic function f and an almost periodicity of f'.
14
Content available remote On strict convexity of the Weyl-Orlicz space of almost periodic functions
Bedouhene F., Morsli M.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2000
|
[Z] 40
33-47
EN
Abstract. In [2], T.R. Hillmann investigated some structural and topo-logical properties of the Besicovitch-Orlicz space (and others like as the Stepanoff and Weyl-Orlicz spaces) and his subspaces of almost periodic functions. In [3], we characterized the strict and uniform convexity of this space. In this paper, the strict convexity property is characterized in the Weyl-Orlicz space of almost periodic functions
15
Content available remote (VC)(n)-almost periodic functions
Stoiński S.
Demonstratio Mathematica
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1999
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Vol. 32, nr 2
377-383
EN
In this note we give the definition and some properties of (VC) (n)-almost periodic functions, i,e, uniformly almost periodic and almost periodic in variation functions with first n derivatives.
16
Content available remote On compactness in variation of almost periodic functions
Stoiński S.
Demonstratio Mathematica
|
1998
|
Vol. 31, nr 1
131-134
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