Geodesic
Uniformly bounded Nemytskij operators generated by set-valued functions between generalized Hölder function spaces
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 31 (2011) no. 2, pp. 183-198.

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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.
Keywords: Nemytskij composition operator, uniformly bounded operator, set-valued function, generalized Hölder function metric space 
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Matkowski, Janusz; Wróbel, Małgorzata. Uniformly bounded Nemytskij operators generated by set-valued functions between generalized Hölder function spaces. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 31 (2011) no. 2, pp. 183-198. http://geodesic.mathdoc.fr/item/DMDICO_2011_31_2_a3/

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