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Mathematics, 2020 This paper is devoted to the study of evolution problems involving fractional flow and time and state dependent maximal monotone operator which is absolutely continuous in variation with respect to the Vladimirov’s pseudo distance.
Charles Castaing +2 more
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Fixed Point Theory and Applications, 2009 We introduce an iterative scheme for finding a common element of the solution set of a maximal monotone operator and the solution set of the variational inequality problem for an inverse strongly-monotone operator in a uniformly smooth and uniformly ...
Somyot Plubtieng, Wanna Sriprad
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Fixed Point Theory and Applications, 2009 We prove strong convergence theorems for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a hemirelatively nonexpansive mapping in a Banach space by using monotone hybrid iteration method.
Chakkrid Klin-eam, Suthep Suantai
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Proximal Decomposition on the Graph of a Maximal Monotone Operator [PDF]
SIAM Journal on Optimization, 1995 We present an algorithm to solve: Find $(x, y) \in A\times A^\bot$ such that $y\in Tx$, where $A$ is a subspace and $T$ is a maximal monotone operator. The algorithm is based on the proximal decomposition on the graph of a monotone operator and we show how to recover Spingarn's decomposition method.
Philippe Mahey +2 more
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NOTES ON GRAPH-CONVERGENCE FOR MAXIMAL MONOTONE OPERATORS [PDF]
Bulletin of the Australian Mathematical Society, 2010 AbstractWe construct a sequence {An} of maximal monotone operators with a common domain and converging, uniformly on bounded subsets, to another maximal monotone operator A; however, the sequence {t−1nAn} fails to graph-converge for some null sequence {tn}.
CIANCIARUSO, Filomena +3 more
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Differential-algebraic inclusions with maximal monotone operators [PDF]
2016 IEEE 55th Conference on Decision and Control (CDC), 2016 The term differential-algebraic inclusions (DAIs) not only describes the dynamical relations using set-valued mappings, but also includes the static algebraic inclusions, and this paper considers the problem of existence of solutions for a class of such dynamical systems described by the inclusion equation for a symmetric positive semi-definite matrix ...
M. Kanat Camlibel +3 more
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On the local boundedness of maximal H-monotone operators [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2017 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.
Calogero, A, Balogh, ZM, Pini, R
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The Local Equicontinuity of a Maximal Monotone Operator [PDF]
Set-Valued and Variational Analysis, 2015 The local equicontinuity of an operator $T:X\rightrightarrows X^{*}$ with proper Fitzpatrick function $φ_{T}$ and defined in a barreled locally convex space $X$ has been shown to hold on the algebraic interior of $\operatorname*{Pr}\,_{X}(\operatorname*{dom}φ_{T})$). The current note presents direct consequences of the aforementioned result with regard
exaly +3 more sources
An Answer to S. Simons’ Question on the Maximal Monotonicity of the Sum of a Maximal Monotone Linear Operator and a Normal Cone Operator [PDF]
Set-Valued and Variational Analysis, 2009 The question whether or not the sum of two maximal monotone operators is maximal monotone under Rockafellar's constraint qualification - that is, whether or not "the sum theorem" is true - is the most famous open problem in Monotone Operator Theory. In his 2008 monograph "From Hahn-Banach to Monotonicity", Stephen Simons asked whether or not the sum ...
Heinz H Bauschke +2 more
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On the maximal monotone operators in Hadamard spaces
OptimizationIn this paper, some topics of monotone operator theory in the setting of Hadamard spaces are investigated. For a fixed element $p$ in a Hadamard space $X$, the notion of $p$-Fenchel conjugate is introduced and a type of the Fenchel-Young inequality is proved.
Ali Moslemipour +2 more
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