Opuscula Mathematica

Opuscula Math.
 27
, no. 1
 (), 13-24
Opuscula Mathematica

On Lipschitzian operators of substitution generated by set-valued functions


Abstract. We consider the Nemytskii operator, i.e., the operator of substitution, defined by \((N \phi)(x):=G(x,\phi(x))\), where \(G\) is a given multifunction. It is shown that if \(N\) maps a Hölder space \(H_{\alpha}\) into \(H_{\beta}\) and \(N\) fulfils the Lipschitz condition then \[G(x,y)=A(x,y)+B(x),\tag{1}\] where \(A(x,\cdot)\) is linear and \(A(\cdot ,y),\, B \in H_{\beta}\). Moreover, some conditions are given under which the Nemytskii operator generated by \((1)\) maps \(H_{\alpha}\) into \(H_{\beta}\) and is Lipschitzian.
Keywords: Nemytskii operator, Hölder functions, set-valued functions, Jensen equation.
Mathematics Subject Classification: 39B99, 47H04, 47H30, 54C60.
Cite this article as:
Jakub Jan Ludew, On Lipschitzian operators of substitution generated by set-valued functions, Opuscula Math. 27, no. 1 (2007), 13-24
 
Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

RSS Feed

horizontal rule

ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

horizontal rule

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.