Geodesic
Monotone relations in Hadamard spaces
Filomat, Tome 33 (2019) no. 19, p. 6347

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DOI

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. 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
DOI : 10.2298/FIL1919347M
Classification : 47H05, 47H04
Keywords: Monotonicity, geodesic space, flat Hadamard spaces, monotone relations, Lipschitz semi-norm 
Ali Moslemipour; Mehdi Roohi; Mohammad Reza Mardanbeigi; Mahdi Azhini. Monotone relations in Hadamard spaces. Filomat, Tome 33 (2019) no. 19, p. 6347 . doi: 10.2298/FIL1919347M
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     title = {Monotone relations in {Hadamard} spaces},
     journal = {Filomat},
     pages = {6347 },
     year = {2019},
     volume = {33},
     number = {19},
     doi = {10.2298/FIL1919347M},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL1919347M/}
}
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