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Uniformly bounded Nemytskij operators generated by set-valued functions between generalized Hölder function spaces

Janusz Matkowski; Małgorzata Wróbel

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2011)

  • Volume: 31, Issue: 2, page 183-198
  • ISSN: 1509-9407

Abstract

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We prove that the generator of any uniformly bounded set-valued Nemytskij operator acting between generalized Hölder function metric spaces, with nonempty compact and convex values is an affine function with respect to the function variable.

How to cite

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Janusz Matkowski, and Małgorzata Wróbel. "Uniformly bounded Nemytskij operators generated by set-valued functions between generalized Hölder function spaces." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 31.2 (2011): 183-198. <http://eudml.org/doc/271174>.

@article{JanuszMatkowski2011,
abstract = {We prove that the generator of any uniformly bounded set-valued Nemytskij operator acting between generalized Hölder function metric spaces, with nonempty compact and convex values is an affine function with respect to the function variable.},
author = {Janusz Matkowski, Małgorzata Wróbel},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {Nemytskij composition operator; uniformly bounded operator; set-valued function; generalized Hölder function metric space; superposition operator},
language = {eng},
number = {2},
pages = {183-198},
title = {Uniformly bounded Nemytskij operators generated by set-valued functions between generalized Hölder function spaces},
url = {http://eudml.org/doc/271174},
volume = {31},
year = {2011},
}

TY - JOUR
AU - Janusz Matkowski
AU - Małgorzata Wróbel
TI - Uniformly bounded Nemytskij operators generated by set-valued functions between generalized Hölder function spaces
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2011
VL - 31
IS - 2
SP - 183
EP - 198
AB - We prove that the generator of any uniformly bounded set-valued Nemytskij operator acting between generalized Hölder function metric spaces, with nonempty compact and convex values is an affine function with respect to the function variable.
LA - eng
KW - Nemytskij composition operator; uniformly bounded operator; set-valued function; generalized Hölder function metric space; superposition operator
UR - http://eudml.org/doc/271174
ER -

References

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  1. [1] J. Appell and P.P. Zabrejko, Nonlinear Superposition Operators, Cambridge University Press, 1990. doi:10.1017/CBO9780511897450 Zbl0701.47041
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  3. [3] V.V. Chistyakov, Lipschitzian superposition operators between spaces of functions of bounded generalized variation with weight, J. Appl. Anal. 6 (2000), 173-186. doi:10.1515/JAA.2000.173 
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  11. [11] J. Matkowski, Uniformly continuous superposition operators in the spaces of bounded variation functions, Math. Nachr. 283 (7) (2010), 1060-1064. Zbl1235.47052
  12. [12] J. Matkowski, Uniformly bounded composition operators between general Lipschitz function normed spaces, (accepted), Top. Math. Nonl. Anal. Zbl1272.47070
  13. [13] J. Matkowski and J. Miś, On a charakterization of Lipschitzian operators of substitution in the space BV[a,b], Math. Nachr. 117 (1984), 155-159. doi:10.1002/mana.3211170111 Zbl0566.47033
  14. [14] K. Nikodem, K-convex and K-concave set-valued functions, Zeszyty Naukowe Politechniki Łódzkiej, Mat. 559, Rozprawy Naukowe 114, 1989. 
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  16. [16] W. Smajdor, Note on Jensen and Pexider functional equations, Demonstratio Math. 32 (1999), 363-376. Zbl0938.39026

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