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Zeitschrift für Analysis und ihre Anwendungen


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Volume 5, Issue 4, 1986, pp. 333–346
DOI: 10.4171/ZAA/202

Published online: 1986-08-31

Maximal Monotone Operators and Saddle Functions I

Eckehard Krauss

We investigate the monotone operator $T_K \subseteq E \times E^*, f \in T_Kx\colon = [–f, f] \in \partial K(x,x)$, which is defined via the subdifferential of a concave-convex saddle function $K$. Our considerations are motivated by the fact that each maximal monotone operator $A$ possesses a representation of the form $A = T_K$. We show that $T_K$ is maximal monotone if and only if $K$ is in a relaxed form skew-symmetric. This allows a generalization of results obtained previously.

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Krauss Eckehard: Maximal Monotone Operators and Saddle Functions I. Z. Anal. Anwend. 5 (1986), 333-346. doi: 10.4171/ZAA/202