Kasperski, Andrzej Modular approximation in \(\widetilde {X}_ \varphi\) by a filtered family of dist-sublinear operators and dist-convex operators. (English) Zbl 0808.46040 Math. Jap. 38, No. 1, 119-125 (1993). 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 Keywords:Musielak-Orlicz function space; boundedness of filtered family of operators; space of multifunctions; dist-sublinear operators; dist-convex operators PDFBibTeX XMLCite \textit{A. Kasperski}, Math. Japon. 38, No. 1, 119--125 (1993; Zbl 0808.46040)