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Journal of Convex Analysis 16 (2009), No. 3, 767--778
Copyright Heldermann Verlag 2009

New Properties of the Variational Sum of Monotone Operators

Yboon García Ramos
Centro de Modelamiento Matemático, Universidad de Chile, Av. Blanco Encalada 2120, 7o Piso, Santiago, Chile

We study the Variational Sum of monotone operators, in particular its relationship with the Extended Sum of monotone operators. First, we establish some new properties of the Variational Sum, among them that this sum has closed graph and convex values. Then, we show that the graph of the Variational Sum always contains the graph of the Extended Sum, and hence, it contains also the graph of the usual sum. An example is given showing that the latter inclusions are proper in general.

Keywords: Monotone operator, extended sum, variational sum.

MSC: 47H05; 52A41, 26B25

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