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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.

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

3 Commentationes Mathematicae

1 Bedouhene F.

1 Kozlowski W. M.

1 Morsli M.

1 Musielak A.

1 2011

2 2005

Wyniki wyszukiwania

On Cauchy Conservative Families of Nonlinear Integral Operators

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

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