Fitzpatrick transform of monotone relations in Hadamard spaces

Moslemipour, Ali; Roohi, Mehdi; Mardanbeigi, Mohammad Reza; Azhini, Mahdi

doi:10.2478/auom-2020-0026

Cited by 2 publications

(3 citation statements)

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“…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. The main aim of this section is to prove a representation result for maximal monotone operators based on elements of Γ ⬫ p (X).…”

Section: Resultsmentioning

confidence: 99%

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Representation of Maximal Monotone Operators in Hadamard Spaces

Moslemipour¹,

Roohi²

2021

Preprint

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This paper is devoted to study some topics of monotone operator theory in the context of Hadamard spaces. For a fixed element p in an Hadamard space X, the notion of p-Fenchel conjugate is introduced and a generalization of Fenchel-Young inequality is proved. Moreover, p-Fitzpatrick transform of a monotone set-valued operator from an Hadamard space X to its linear dual space X ◊ and its main properties are investigated. Finally, a characterization result for maximality of monotone operator T ∶ X ⊸ X ◊ , based on certain classes of proper, convex, l.s.c. extended real-valued function h on X × X ◊ , is given.

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Section: Resultsmentioning

confidence: 99%

“…As we will see, this mapping is useful for simplifying many results of this paper. Some properties of p-coupling function can be found in [17]. Moreover, define the mapping…”

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confidence: 99%