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2 Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2 2005

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On Cauchy Conservative Families of Nonlinear Integral Operators

Musielak A.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2005

Vol. 45, [Z] 1

1--11

Let [formula] be nonlinear integral operators of the from (2). There is estimated the expresion [formula] where ρ is a modular on the space [formula]. This is applied in order to obtain a theorem concerning modular conservatitivy of a family [formula] of operators T of the form (2).

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

Bedouhene F., Morsli M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2005

Vol. 45, [Z] 1

13--23

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.