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Regular Maximal Monotone Operators
Set-Valued Analysis, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Verona, Andrei, Verona, Maria E.
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Distances between Maximal Monotone Operators
Siberian Mathematical Journal, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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About the Maximal Monotonicity of the Generalized Sum of Two Maximal Monotone Operators
Set-Valued and Variational Analysis, 2011In this paper, the authors present some regularity conditions to ensure the maximal mo\-no\-to\-ni\-ci\-ty of the generalized sum of two strongly-representable monotone operators of closedness and interior point type. The obtained theorems extend some recent results.
László, Szilárd +1 more
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Maximal Monotonicity for the Precomposition with a Linear Operator
SIAM Journal on Optimization, 2007We give the weakest constraint qualification known to us that ensures the maximal monotonicity of the operator $A^* \circ T \circ A$ when $A$ is a linear continuous mapping between two reflexive Banach spaces and $T$ is a maximal monotone operator. As a special case we get the weakest constraint qualification that guarantees the maximal monotonicity of
Radu Ioan Bot +2 more
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Maximal Hyperclones Determined by Monotone Operations
2011 41st IEEE International Symposium on Multiple-Valued Logic, 2011Let A be a finite set. It is well known that every bounded partial order relation determines a maximal clone on A and every non-trivial partial order relation determines a maximal partial clone on A. In this paper we describe a class of maximal hyper clones that are determined by bounded partial order relations on A.
Jelena Colic +2 more
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Characterizations of maximal monotone operators
Nonlinear Analysis: Theory, Methods & Applications, 1992Die Verfasser betrachten monotone Operatoren \(T: A\to 2^{X^*}\) von einer Teilmenge \(A\subseteq X\) eines Banach-Raumes \(X\) in die Menge aller Teilmengen seines Dualraumes \(X^*\). Ist \(A\) offen, dann ist bekannterweise die maximale Monotonie von \(T\) zu jeder der folgenden Eigenschaften (1), (2) äquivalent: (1) \(T\) ist konvex- und \(w ...
Verona, Maria Elena, Verona, Andrei
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A Family of Enlargements of Maximal Monotone Operators
Set-Valued Analysis, 2000The author introduces a family of enlargements of maximal monotone operators. He characterizes the biggest and the smallest enlargement belonging to this family and discusses some general properties of the members of a subfamily formally closer to the \(\varepsilon\)-subdifferential. He proves the existence of maximal elements.
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Cyclical monotonicity of maximal monotone step operators
Boletim da Sociedade Brasileira de Matemática, 1982Let 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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On maximal \(\psi\)-monotonicity of sums of operators.
1998Summary: We give some sufficient conditions for the maximal \(\psi\)-monotonicity of sums of \(\psi\)-monotone operators. The results are obtained in general topological vector spaces. An existence result for equilibrium problems is also included.
Oettli, Werner, Riahi, Hassan
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On the Maximality of the Sum of Two Maximal Monotone Operators
2018Let E be a real reflexive Banach space, E∗ be the dual space of E and \(T: D(T)\subseteq E\to 2^{E^{*}}\), \(S:D(S)\subseteq E\to 2^{E^*}\) be two maximal monotone operators such that D(T) ∩ D(S) ≠ ∅. Assume that there exist x0 ∈ E, r > 0, λ0 > 0 such that inff ∈ Tx(f, x − x0) is lower bounded on each bounded subset of D(T) and, if, for each y ∈ B(x0 ...
Yuqing Chen +2 more
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