×

Modular approximation in \(\widetilde {X}_ \varphi\) by a filtered family of dist-sublinear operators and dist-convex operators. (English) Zbl 0808.46040

Summary: We introduce the notion of \((\text{dist},{\mathcal V})\)-boundedness of a filtered family of operators in a space \(\widetilde X_ \varphi\) of multifunctions. This notion is used to get the convergence theorems for families of dist-sublinear operators and families of dist-convex operators.

MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46A80 Modular spaces
54C60 Set-valued maps in general topology
28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections
PDFBibTeX XMLCite