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AN OPERATOR INEQUALITY FOR OPERATOR MONOTONE FUNCTIONS (Operator monotone functions and related topics)

open access: yesAN OPERATOR INEQUALITY FOR OPERATOR MONOTONE FUNCTIONS (Operator monotone functions and related topics)
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Regular Maximal Monotone Operators

Set-Valued Analysis, 1998
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Verona, Andrei, Verona, Maria E.
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Operations with monotone operators and the monotonicity of the resulting operators

Monatshefte für Mathematik, 2015
Let \(\mathcal H\) be a Hilbert space \({\mathcal D} \subseteq {\mathcal H}, \eta \in (-1,1)\) and \(T: {\mathcal D} \rightarrow {\mathcal H}\) be given. The authors say \(T\) to be \textit{\(\eta\)-increasing} if \(\langle Tx-Ty, x-y \rangle \geq \eta \parallel Tx-Ty \parallel \parallel x-y \parallel\) for all \(x,y \in {\mathcal D}\). For \(T\) to be
Daniela Marian   +2 more
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Characterization of approximate monotone operators

2022
The authors study approximate monotone operators. They show that a well-known property of monotone operators, namely, representing by convex functions, remains valid for this larger class of operators. In this general framework, results of \textit{S.
Rezaei, Mahboubeh, Mirsaney, Zahra Sadat
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Distances between Maximal Monotone Operators

Siberian Mathematical Journal, 2023
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Operator Inequalities Involving Operator Monotone Functions

2021
In this chapter, we gather improvements of known operator inequalities involving positive linear maps, geometric means, operator monotone functions, and doubly concave functions. We note that these types of operator inequalities have essential applications in the theory of functional equations in non-euclidean geometry.
Mohammad Bagher Ghaemi   +3 more
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Cyclical monotonicity of maximal monotone step operators

Boletim da Sociedade Brasileira de Matemática, 1982
Let X and Y be two locally convex Hausdorff topological vector spaces paired by a bilinear form \(\). A multimapping \(T: X\to 2^ y\) is said to be a locally step operator if each \(x\in X\) has a neighborhood U such that \(\{Ty\}_{y\in U}\) is a finite family of sets, that is, if locally T takes a finite number of set values.
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