Geodesic
Monotonicity of sets in Hadamard spaces from polarity point of view
Filomat, Tome 36 (2022) no. 13, p. 4459

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DOI

This paper is devoted to introduce and investigate the notion of monotone sets in Hadamard spaces. First, flat Hadamard spaces are introduced and investigated. It is shown that an Hadamard space X is flat if and only if X × X ♢ has F l-property, where X ♢ is the linear dual of X. Moreover, monotone and maximal monotone sets are introduced and also monotonicity from polarity point of view is considered. Some characterizations of (maximal) monotone sets, specially based on polarity, are given. Finally, it is proved that any maximal monotone set is sequentially bw×∥ · ∥ ♢-closed in X × X ♢ .
DOI : 10.2298/FIL2213459M
Classification : 47H05, 47H04, 49J40
Keywords: Monotone sets, maximal monotone sets, polarity, flat Hadamard space, R-tree 
Ali Moslemipour; Mehdi Roohi. Monotonicity of sets in Hadamard spaces from polarity point of view. Filomat, Tome 36 (2022) no. 13, p. 4459 . doi: 10.2298/FIL2213459M
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     title = {Monotonicity of sets in {Hadamard} spaces from polarity point of view},
     journal = {Filomat},
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     year = {2022},
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     doi = {10.2298/FIL2213459M},
     language = {en},
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