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2 Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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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).

On consistency of summability methods generated by nonlinear integral operators

Tomasz B.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1999

[Z] 39

197-205

Let r,n be two modulars on L(G), and let W be an abstract set of indices. For nonlinear integral op-erators T(w) and S(w) on L(G), we give sufficient conditions for two methods of summability gen-erated by T(w) and S(w) to be consistent for sequences (f(w)) of functions of L(G), in the sense of modular r.