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ArticleOriginal scientific text

Title

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

Authors 1, 2, 3

Affiliations

  1. Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland
  2. Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
  3. Institute of Mathematics and Computer Science, Jan Dlugosz University, 42-200 Częstochowa, Poland

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.

Keywords

ENG
Nemytskij composition operator, uniformly bounded operator, set-valued function, generalized Hölder function metric space

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Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2011/31/2
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Pages:
183-198
Main language of publication
English
Received
2011-05-30
Published
2011

DOI: 10.7151/dmdico.1134

Exact and natural sciences