Variational and Extended Sums of Monotone Operators

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Abstract

In this article we show that the notion of variational sum of maximal monotone operators, introduced by Attouch, Baillon and Théra in [3] in the setting of Hilbert spaces, can be successfully extended to the case of reflexive Banach spaces, preserving all of its properties. We make then a comparison with the usual pointwise sum and with the notion of extended sum proposed in our paper [26].