On Lipschitzian operators of substitution generated by set-valued functions
Titel:
On Lipschitzian operators of substitution generated by set-valued functions
Auteur:
Jakub Jan Ludew
Verschenen in:
Opuscula mathematica
Paginering:
Jaargang 27 (2007) nr. 1 pagina's 13-24
Jaar:
2007
Inhoud:
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 $G(x, y)=A(x, y)+B(x)$ (1), where $A(x,·)$ is linear and $A(·, y)$, $B \in H_{\beta}$. Moreover, some conditions are given under which the Nemytskii operator generated by (1) maps $H_{\alpha}$ into $H_{\beta}$ and is Lipschitzian.
Uitgever:
AGH University of Science and Technology (provided by DOAJ)
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