arXiv subjects

Ali Moslemipour

Publications and source records attributed to Ali Moslemipour.

3 recordsLinked to original sources

arXiv2021

On the Maximal Monotone Operators in Hadamard Spaces

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.

math.FA↗

arXiv2019

Monotone Relations in Hadamard Spaces

In this paper, the notion of $\mathcal{W}$-property for subsets of $X\times X^{\lozenge}$ is introduced and investigated, where $X$ is an Hadamard space and $X^{\lozenge}$ is its linear dual space. It is shown that an Hadamard space $X$ is flat if and only if $X\times X^{\lozenge}$ has $\mathcal{W}$-property. Moreover, the notion of monotone relation from an Hadamard space to its linear dual space is introduced. Finally, a characterization result for monotone relations with $\mathcal{W}$-property (and hence in flat Hadamard spaces) is proved.

math.FA↗

arXiv2019

Monotonicity of sets in Hadamard spaces from polarity point of view

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 $X\times X^\medlozenge$ has $\mathcal{F}_l$-property, where $X^\medlozenge$ 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 $bw\times${$\|\cdot\|_\loz$}-closed in $X\times X^\medlozenge$.

math.FA↗