Notes on approximation in the Musielak-Orlicz sequence spaces of multifunctions

Andrzej Kasperski

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 1, page 19-24
  • ISSN: 0010-2628

Abstract

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

How to cite

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Kasperski, Andrzej. "Notes on approximation in the Musielak-Orlicz sequence spaces of multifunctions." Commentationes Mathematicae Universitatis Carolinae 36.1 (1995): 19-24. <http://eudml.org/doc/247710>.

@article{Kasperski1995,
abstract = {We introduced the notion of $(\{\mathbf \{X\}\},\operatorname\{dist\},\{\mathcal \{V\}\})$-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 $\{\mathbf \{X\}\}$-linear operators, $\{\mathbf \{X\}\}$-dist-sublinear operators and $\{\mathbf \{X\}\}$-dist-convex operators. Also, we prove that $X_\{\varphi \}$ is complete.},
author = {Kasperski, Andrzej},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Musielak-Orlicz space; multifunction; modular space of multifunctions; approximation; singular kernel; modular space; Musielak-Orlicz sequence space; approximation},
language = {eng},
number = {1},
pages = {19-24},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Notes on approximation in the Musielak-Orlicz sequence spaces of multifunctions},
url = {http://eudml.org/doc/247710},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Kasperski, Andrzej
TI - Notes on approximation in the Musielak-Orlicz sequence spaces of multifunctions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 1
SP - 19
EP - 24
AB - We introduced the notion of $({\mathbf {X}},\operatorname{dist},{\mathcal {V}})$-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 ${\mathbf {X}}$-linear operators, ${\mathbf {X}}$-dist-sublinear operators and ${\mathbf {X}}$-dist-convex operators. Also, we prove that $X_{\varphi }$ is complete.
LA - eng
KW - Musielak-Orlicz space; multifunction; modular space of multifunctions; approximation; singular kernel; modular space; Musielak-Orlicz sequence space; approximation
UR - http://eudml.org/doc/247710
ER -

References

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  1. Kasperski A., Modular approximation by a filtered family of sublinear operators, Commentationes Math. XXVII (1987), 109-114. (1987) Zbl0636.46025MR0910964
  2. Kasperski A., Modular approximation in X̰ ϕ by a filtered family of X̰ ϕ -linear operators, Functiones et Approximatio XX (1992), 183-187. (1992) MR1201727
  3. Kasperski A., Modular approximation in X̰ ϕ by a filtered family of dist-sublinear operators and dist-convex operators, Mathematica Japonica 38 (1993), 119-125. (1993) MR1204190
  4. Kasperski A., Approximation of elements of the spaces X ϕ 1 and X ϕ by nonlinear singular kernels, Annales Math. Silesianae, Vol. 6, Katowice, 1992, pp. 21-29. Zbl0821.41021MR1217338
  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. Zbl0471.46017MR0650267
  7. Musielak J., Orlicz Spaces and Modular Spaces, Lecture Notes in Mathematics, Vol. 1034, Springer-Verlag, Berlin, 1983. Zbl0557.46020MR0724434

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