Results 231 to 240 of about 544 (259)

A Family of Enlargements of Maximal Monotone Operators

Set-Valued Analysis, 2000
The 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, 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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On the Maximality of the Sum of Two Maximal Monotone Operators

2018
Let 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, Yeol Je Cho, Themistocles M. Rassias   +2 more
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On maximal \(\psi\)-monotonicity of sums of operators.

1998
Summary: 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

2018
In 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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Maximal monotone operators and maximal monotone functions for equilibrium problems

2008
This 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, Yasunori Kimura, Wataru Takahashi   +2 more
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Equilibrium of Maximal Monotone Operator in a Given Set

Discussiones Mathematicae. Differential Inclusions, Control and Optimization, 2000
Let \(C\) 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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On the Range of Maximal Monotone Operators in Nonreflexive Spaces

Mathematische Nachrichten, 1985
Results concerning existence of solutions to the equation \(\theta\in Ax\), where \(A: E\to 2^ F\) is a maximal monotone (or a some what more general) mapping are considered. Here E and F constitute a dual system of real linear spaces (i.e., a mondegenerate bilinear form \(\) exists on \(E\times F)\).
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On the Maximality of the Sum of Monotone Operators

Mathematische Nachrichten, 1981
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Maximal Monotone Operators

2007
Regina S. Burachik, Alfredo N. Iusem
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