Notes on approximation in the Musielak-Orlicz sequence spaces of multifunctions
Kasperski, Andrzej
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995), p. 19-24 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

We introduced the notion of $({\bold X},\operatorname{dist},{\Cal V})$-boundedness of a filtered family of operators in the Musielak-Orlicz sequence space $X_{\varphi }$ of multifunctions. This notion is used to get the convergence theorems for the families of ${\bold X}$-linear operators, ${\bold X}$-dist-sublinear operators and ${\bold X}$-dist-convex operators. Also, we prove that $X_{\varphi }$ is complete.

Publié le : 1995-01-01
Classification:  28B20,  41A65,  46E30,  54C60 
@article{118728,
     author = {Andrzej Kasperski},
     title = {Notes on approximation in the Musielak-Orlicz sequence spaces of multifunctions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {36},
     year = {1995},
     pages = {19-24},
     zbl = {0832.54021},
     mrnumber = {1334410},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118728}
}

Kasperski, Andrzej. Notes on approximation in the Musielak-Orlicz sequence spaces of multifunctions. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 19-24. http://gdmltest.u-ga.fr/item/118728/

Kasperski A. Modular approximation by a filtered family of sublinear operators, Commentationes Math. XXVII (1987), 109-114. (1987) | MR 0910964 | Zbl 0636.46025

Kasperski A. Modular approximation in $\utilde{X}_{\varphi }$ by a filtered family of $\utilde{X}_{\varphi }$-linear operators, Functiones et Approximatio XX (1992), 183-187. (1992) | MR 1201727

Kasperski A. Modular approximation in $\utilde{X}_{\varphi }$ by a filtered family of dist-sublinear operators and dist-convex operators, Mathematica Japonica 38 (1993), 119-125. (1993) | MR 1204190

Kasperski A. Approximation of elements of the spaces $X^{1}_{\varphi }$ and $X_{\varphi }$ by nonlinear singular kernels, Annales Math. Silesianae, Vol. 6, Katowice, 1992, pp. 21-29. | MR 1217338 | Zbl 0821.41021

Kasperski A. Notes on approximation in the Musielak-Orlicz space of multifunctions, Commentationes Math., in print.

Musielak J. Modular approximation by a filtered family of linear operators, ``Functional Analysis and Approximation, Proc. Conf. Oberwolfach, August 9-16, 1980'', BirkhäuserVerlag, Basel 1981, pp. 99-110. | MR 0650267 | Zbl 0471.46017

Musielak J. Orlicz Spaces and Modular Spaces, Lecture Notes in Mathematics, Vol. 1034, Springer-Verlag, Berlin, 1983. | MR 0724434 | Zbl 0557.46020