Firmly Nonexpansive Mappings and Maximally Monotone Operators: Correspondence and Duality [PDF]
Set-Valued and Variational Analysis, 2011 The notion of a firmly nonexpansive mapping is central in fixed point theory because of attractive convergence properties for iterates and the correspondence with maximal monotone operators due to Minty. In this paper, we systematically analyze the relationship between properties of firmly nonexpansive mappings and associated maximal monotone operators.
Bauschke, Heinz H. +2 more
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Nonlinear variational inequalities and maximal monotone mappings in Banach spaces
Mathematische Annalen, 1969 Felix E Browder, Browder Felix E
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A note on Solodov and Tseng’s methods for maximal monotone mappings
Journal of Computational and Applied Mathematics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jinling Zhao, Qingzhi Yang, Hongxiu Gao
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Strong Convergence of Monotone Hybrid Method for Maximal Monotone Operators and Hemirelatively Nonexpansive Mappings [PDF]
Fixed Point Theory and Applications, 2009 AbstractWe 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.
Klin-eam Chakkrid, Suantai Suthep
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Topological degree and application to a parabolic variational inequality problem
International Journal of Mathematics and Mathematical Sciences, 2001 We are interested in constructing a topological degree for operators of the form F=L+A+S, where L is a linear densely defined maximal monotone map, A is a bounded maximal monotone operators, and S is a bounded demicontinuous map of class (S+) with ...
A. Addou, B. Mermri
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Well-Posedness and Output Regulation for Implicit Time-Varying Evolution Variational Inequalities [PDF]
SIAM Journal of Control and Optimization, 2016 A class of evolution variational inequalities (EVIs), which comprises ordinary differential equations (ODEs) coupled with variational inequalities (VIs) associated with time-varying set-valued mappings, is proposed in this paper.
A. Tanwani, B. Brogliato, C. Prieur
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An optimal transport problem with backward martingale constraints motivated by insider trading [PDF]
The Annals of Applied Probability, 2019 We study a single-period optimal transport problem on $\mathbb{R}^2$ with a covariance-type cost function $c(x,y) = (x_1-y_1)(x_2-y_2)$ and a backward martingale constraint.
D. Kramkov, Yan Xu
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A note on the degree for maximal monotone mappings in finite dimensional spaces
Applied Mathematics Letters, 2009 The authors attempt to give an easy way to define the topological degree of a maximal monotone mapping as the limit of the classical Brouwer degrees of the Yosida approximations. Moreover, a homotopy property for the degree of a maximal monotone mapping and also for the degree of a subdifferential of a continuous convex function is obtained.
Chen, Yuqing +3 more
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A Method of approximation for a zero of the sum of maximally monotone mappings in Hilbert spaces
Arab Journal of Mathematical Sciences, 2020 Our purpose of this study is to construct an algorithm for finding a zero of the sum of two maximally monotone mappings in Hilbert spaces and discus its convergence. The assumption that one of the mappings is α-inverse strongly monotone is dispensed with. In addition, we give some applications to the minimization problem.
Getahun Bekele Wega, Habtu Zegeye
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Convergence of Paths for Perturbed Maximal Monotone Mappings in Hilbert Spaces
Fixed Point Theory and Applications, 2011 AbstractLet "Equation missing" be a Hilbert space and "Equation missing" a nonempty closed convex subset of "Equation missing". Let "Equation missing" be a maximal monotone mapping and "Equation missing" a bounded demicontinuous strong pseudocontraction. Let "Equation missing" be the unique solution to the equation "Equation missing".
Zhou Haiyun +3 more
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