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arXiv · 2106.11085

On the Maximal Monotone Operators in Hadamard Spaces

Ali Moslemipour·Mehdi Roohi·Jen-Chih Yao
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Abstract

In this paper, some topics of monotone operator theory in the setting of Hadamard spaces are investigated. For a fixed element $p$ in a Hadamard space $X$, the notion of $p$-Fenchel conjugate is introduced and a type of the Fenchel-Young inequality is proved. Moreover, we examine the $p$-Fitzpatrick transform and its main properties for monotone set-valued operators in Hadamard spaces. Furthermore, some relations between maximal monotone operators and certain classes of proper, convex, l.s.c. extended real-valued functions on $X\times X^{\scalebox{0.7}{$^{\lozenge}$}}$, are given.

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Ali Moslemipour, Mehdi Roohi, Jen-Chih Yao. 2021-06-21. On the Maximal Monotone Operators in Hadamard Spaces. https://doi.org/10.1080/02331934.2024.2341940

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