# 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

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topJanusz 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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