On Lipschitzian operators of substitution generated by set-valued functions
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),...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2007-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | http://www.opuscula.agh.edu.pl/vol27/1/art/opuscula_math_2702.pdf |