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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 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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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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Coderivatives of Maximal Monotone Operators
2018In this chapter we employ the tools of variational analysis and generalized differentiation developed above to study global and local monotonicity of set-valued operators.
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On the maximality of the sum of two maximal monotone operators
Nonlinear Analysis: Theory, Methods & Applications, 1981Abstract : A wide variety of problems involving nonlinear partial differential equations, subject to boundary conditions, may be shown to have solutions by establishing that the associated differential operators satisfy a certain technical condition. This condition, called maximal monotonicity, allows the use of a well developed abstract theory which ...
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Maximal monotone operators and maximal monotone functions for equilibrium problems
2008This paper investigates relationships between the problem of finding a zero of a maximal monotone operator and the equilibrium problem. Given a bivariate function \(f\) associated with an equilibrium problem, and using results from [\textit{E. Blum} and \textit{W. Oettli}, Math. Stud. 63, No.
Koji Aoyama +2 more
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Equilibrium of Maximal Monotone Operator in a Given Set
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, 2000Let \(C\) be a nonempty weakly compact convex subset of a real Banach space \(E\) and \(f: E\to\overline{\mathbb{R}}\) be a lower semi-continuous convex function. The question about the equality \[ \inf_E f= \inf_C f \] can be characterized by the following two different conditions: \[ \forall x\not\in C\;\exists c\in C:f'(x; c-x)\leq 0\qquad (\text ...
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An iterative algorithm for maximal monotone multivalued operator equations
Acta Mathematica Scientia, 2001Jinsheng Xiao
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