Monotone relations in Hadamard spaces
In this paper, the notion of W-property for subsets of X 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 X? has W-property. Moreover, the notion of monotone relation from an Hadamard space to its linear dual space is introduced. A characterization result for monotone relations with W-property (and hence in flat Hadamard spaces) is given. Finally, a type of Debrunner-Flor Lemma concerning extension of monotone relations in Hadamard spaces is proved.
2020 ◽
Vol 28
(2)
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pp. 173-193
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1990 ◽
Vol 32
(3)
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pp. 273-276
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2018 ◽
Vol 9
(1)
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pp. 1-27
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