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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 the Existence of Common Fixed Points for Semigroups of Nonlinear Mappings in Modular Function Spaces

63%

Kozlowski W. M.

Commentationes Mathematicae

2011

tom 51

nr 1

Let $C$ be a $\rho$-bounded, $\rho$-closed, convex subset of a modular function space $L_\rho$. We investigate the existence of common fixed points for semigroups of nonlinear mappings $T_t\colon C\to C$, i.e. a family such that $T_0(x) = x$, $T_{s+t} = T_s (T_t (x))$, where each $T_t$ is either $\rho$-contraction or $\rho$-nonexpansive. We also briefly discuss existence of such semigroups and touch upon applications to differential equations.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Commentationes Mathematicae

1 Bardaro C.

1 Kozlowski W. M.

1 Musielak J.

1 Vinti G.

1 2011

1 1996

Wyniki wyszukiwania

Approximation by nonlinear integral operators in some modular function spaces

On the Existence of Common Fixed Points for Semigroups of Nonlinear Mappings in Modular Function Spaces