Browsing by Subject "Jensen equation"

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Access status: Open Access ,
On Lipschitzian operators of substitution generated by set-valued functions
(2007) Ludew, Jakub Jan
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 $A(x,\cdot)$ 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.
Access status: Open Access ,
Uniformly continuous set-valued composition operators in the spaces of functions of bounded variation in the sense of Wiener
(2010) Azócar Bates, Luis Antonio; Guerrero, José Atilio; Matkowski, Janusz; Merentes Díaz, Nelson José
We show that the one-sided regularizations of the generator of any uniformly continuous and convex compact valued composition operator, acting in the spaces of functions of bounded variation in the sense of Wiener, is an affine function.