Article
Full entry |
PDF
(0.1 MB)
Feedback
PDF
(0.1 MB)
Feedback
Keywords:
Musielak-Orlicz space; multifunction; modular space of multifunctions; approximation; singular kernel
Musielak-Orlicz space; multifunction; modular space of multifunctions; approximation; singular kernel
Summary:
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.
References:
[1] Kasperski A.: Modular approximation by a filtered family of sublinear operators. Commentationes Math. XXVII (1987), 109-114. MR 0910964 | Zbl 0636.46025
[2] 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. MR 1201727
[3] 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. MR 1204190
[4] 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
[5] Kasperski A.: Notes on approximation in the Musielak-Orlicz space of multifunctions. Commentationes Math., in print.
[6] 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
[7] Musielak J.: Orlicz Spaces and Modular Spaces. Lecture Notes in Mathematics, Vol. 1034, Springer-Verlag, Berlin, 1983. MR 0724434 | Zbl 0557.46020
Search
Partner of
