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Approximation by nonlinear integral operators in some modular function spaces

100%

Bardaro C., Musielak J., Vinti G.

Annales Polonici Mathematici

1996

tom 63

nr 2

173-182

Let G be a locally compact Hausdorff group with Haar measure, and let L⁰(G) be the space of extended real-valued measurable functions on G, finite a.e. Let ϱ and η be modulars on L⁰(G). The error of approximation ϱ(a(Tf - f)) of a function $f ∈ (L⁰(G))_{ϱ+η} ∩ Dom T$ is estimated, where $(Tf)(s) = ∫_G K(t-s,f(t))dt$ and K satisfies a generalized Lipschitz condition with respect to the second variable.

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On Cauchy Conservative Families of Nonlinear Integral Operators

100%

Musielak A.

Commentationes Mathematicae

2005

tom 45

nr 1

Let $T_1, T_2$ be nonlinear integral operators of the form (2). There is estimated the expression $\rho [\alpha(T_1 f - T_2 g)]$, where $\rho$ is a modular on the space $L^0(\Omega)$. This is applied in order to obtain a theorem concerning modular conservativity of a family $T = (T_w)_{w\in W}$ of operators $T$ w of the form (2).

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

100%

Bedouhene F., Morsli M.

Commentationes Mathematicae

2005

tom 45

nr 1

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.

Ograniczanie wyników

2 Commentationes Mathematicae

1 Annales Polonici Mathematici

1 Bardaro C.

1 Bedouhene F.

1 Morsli M.

1 Musielak A.

1 Musielak J.

1 Vinti G.

2 2005

1 1996

Wyniki wyszukiwania

Approximation by nonlinear integral operators in some modular function spaces

On Cauchy Conservative Families of Nonlinear Integral Operators

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