Monotone relations in Hadamard spaces

Abstract

In this paper, the notion of W-property for subsets of X × X ♦ is introduced and investigated, where X is an Hadamard space and X ♦ is its linear dual space. It is shown that an Hadamard space X is flat if and only if X × X ♦ has W-property. Moreover, the notion of monotone relation from an Hadamard space to its linear dual space is introduced. Finally, a characterization result for monotone relations with W-property (and hence in flat Hadamard spaces) is proved.

Representation of Maximal Monotone Operators in Hadamard Spaces

“…Recently, the notions of monotone relations and maximal monotone relations from an Hadamard space to its linear dual space are introduced and their basic properties are investigated in [16,17]. Fitzpatrick transform of monotone relations in Hadamard spaces is introduced in [17] and it is shown that the Fitzpatrick transform of a certain class of monotone relations is proper, convex and lower semi-continuous.…”