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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1134,
author = {Janusz Matkowski and Ma\l gorzata Wr\'obel},
title = {Uniformly bounded Nemytskij operators generated by set-valued functions between generalized H\"older function spaces},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {31},
year = {2011},
pages = {183-198},
zbl = {1264.47070},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1134}
}
Janusz Matkowski; Małgorzata Wróbel. Uniformly bounded Nemytskij operators generated by set-valued functions between generalized Hölder function spaces. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 31 (2011) pp. 183-198. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1134/
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