Results 1 to 10 of about 1,143 (203)
On the convergence of maximal monotone operators [PDF]
Proceedings of the American Mathematical Society, 2005 We study the convergence of maximal monotone operators with the help of representations by convex functions. In particular, we prove the convergence of a sequence of sums of maximal monotone operators under a general qualification condition of the Attouch–Brezis type.
Jean‐Paul Penot, Constantin Zălinescu
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On the extensions to the bidual of a maximal monotone operator [PDF]
Proceedings of the American Mathematical Society, 1977 An example is given which shows that a maximal monotone operator from a Banach space X to its dual X ∗ {X^\ast } may have several extensions into a maximal monotone operator from X ∗ ∗ {X^{\ast \ast }} to
Jean–Pierre Gossez
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Maximality of the sum of a maximally monotone linear relation and a maximally monotone operator [PDF]
Set-Valued and Variational Analysis, 2012 16 pages.
Jonathan M. Borwein, Liangjin Yao
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Rectangularity and paramonotonicity of maximally monotone operators [PDF]
Optimization, 2012 Maximally monotone operators play a key role in modern optimization and variational analysis. Two useful subclasses are rectangular (also known as star monotone) and paramonotone operators, which were introduced by Brezis and Haraux, and by Censor, Iusem and Zenios, respectively. The former class has useful range properties while the latter class is of
Heinz H. Bauschke +2 more
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Maximal monotone operators with non-maximal graphical limit
Examples and Counterexamples, 2022 We present a counterexample showing that the graphical limit of maximally monotone operators might not be maximally monotone. We also characterize the directional differentiability of the resolvent of an operator B in terms of existence and maximal ...
Gerd Wachsmuth
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International Journal of Mathematics and Mathematical Sciences, 2011 We prove strong and weak convergence theorems of modified hybrid proximal-point algorithms for finding a common element of the zero point of a maximal monotone operator, the set of solutions of equilibrium problems, and the set of solution of the ...
Kriengsak Wattanawitoon, Poom Kumam
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On the maximality of sums of nonlinear monotone operators [PDF]
Transactions of the American Mathematical Society, 1970 R. T. Rockafellar
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On sum of monotone operator of type (FPV) and a maximal monotone operator
New Trends in Mathematical Science, 2016 In the setting of a general real Banach space, we prove that the sum of a monotone operator A of type (FPV) and a maximal monotone operator B is maximal with domA∩ int domB6 φ and either domB is open or for any x ∈ domA∩ int domB, kx ∗ k ≤ |B(x)|, x ∗ ∈ A(x).
Dillip K. Pradhan, S. R. Pattanaik
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On the local boundedness of maximal H--monotone operators [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2016 In this paper we prove that maximal H-monotone operators $T:H^n\rightrightarrows V_1$ whose domain is all the Heisenberg group $H^n$ are locally bounded. This implies that they are upper semicontinuous. As a consequence, maximal H-monotonicity of an operator on $H^n$ can be characterized by a suitable version of Minty's type theorem.
Zoltán M. Balogh +2 more
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Corrigendum to “Quantitative and stability study of the evolution of a thermoelastic body” [MethodsX 10 (2023) 101983] [PDF]
MethodsXWe prove the existence and uniqueness of a solution to a system of equations describing the evolution of a linear thermoelastic body by using a semi-group method. Moreover, the uniform exponential stability of the solution is shown in a particular case. •
Pascal H. Zinsou +2 more
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