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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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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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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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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 Range of Maximal Monotone Operators in Nonreflexive Spaces
Mathematische Nachrichten, 1985Results 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 Fractional Evolution Inclusion Coupled with a Time and State Dependent Maximal Monotone Operator
Set-Valued and Variational Analysis, 2021Charles Castaing +2 more
exaly
On the Maximality of the Sum of Monotone Operators
Mathematische Nachrichten, 1981openaire +2 more sources
Monotone perturbations of maximal monotone operators
Nonlinear Analysis: Theory, Methods & Applications, 1979openaire +2 more sources