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Some results about perturbed maximal monotone mappings
Computers & Mathematics with Applications, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Strong Convergence Theorems for Maximal Monotone Operators with Nonspreading Mappings in a Hilbert Space [PDF]
Abstract and Applied Analysis, 2012 We prove the strong convergence theorems for finding a common element of the set of fixed points of a nonspreading mapping T and the solution sets of zero of a maximal monotone mapping and an α‐inverse strongly monotone mapping in a Hilbert space.
Liu, Hongjie +2 more
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Gossez’s skew linear map and its pathological maximally monotone multifunctions [PDF]
Proceedings of the American Mathematical Society, 2019 In this note, we give a generalization of Gossez’s example of a maximally monotone multifunction such that the closure of its range is not convex, using more elementary techniques than in Gossez’s original papers. We also discuss some new properties of Gossez’s skew linear operator and its adjoint.
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Strong Convergence Theorem by Monotone Hybrid Algorithm for Equilibrium Problems, Hemirelatively Nonexpansive Mappings, and Maximal Monotone Operators [PDF]
Fixed Point Theory and Applications, 2008 AbstractWe introduce a new hybrid iterative algorithm for finding a common element of the set of fixed points of hemirelatively nonexpansive mappings and the set of solutions of an equilibrium problem and for finding a common element of the set of zero points of maximal monotone operators and the set of solutions of an equilibrium problem in a Banach ...
Cheng Yun, Tian Ming
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Maximal monotonicity of piecewise polyhedral mappings
Maximally monotone mappings that are piecewise polyhedral arise from subdifferentials of convex functions and saddle functions that are piecewise linear-quadratic and enter into algorithmic constructions of importance in linear-quadratic optimization and associated splitting methods.
Li, Xudong +2 more
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Nonlinear Robin problems with unilateral constraints and dependence on the gradient
Electronic Journal of Differential Equations, 2018 We consider a nonlinear Robin problem driven by the p-Laplacian, with unilateral constraints and a reaction term depending also on the gradient (convection term). Using a topological approach based on fixed point theory (the Leray-Schauder alternative
Nikolaos S. Papageorgiou +2 more
doaj
Farthest points and the farthest distance map
, 2005 In this paper, we consider farthest points and the farthest distance map of a closed bounded set in a Banach space. We show, inter alia, that a strictly convex Banach space has the Mazur-like intersection property for weakly compact sets if and only if ...
P. Bandyopadhyay, S. Dutta
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Coderivative characterizations of maximal monotonicity for set-valued mappings
, 2015 This paper concerns generalized differential characterizations of maximal monotone set-valued mappings. Using advanced tools of variational analysis, we establish coderivative criteria for maximal monotonicity of set-valued mappings, which seem to be the first infinitesimal characterizations of maximal monotonicity outside the single-valued case.
Chieu, N. H. +3 more
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Convergence Theorems for Maximal Monotone Operators, Weak Relatively Nonexpansive Mappings and Equilibrium Problems [PDF]
Journal of Applied Mathematics, 2012 We introduce hybrid‐iterative schemes for solving a system of the zero‐finding problems of maximal monotone operators, the equilibrium problem, and the fixed point problem of weak relatively nonexpansive mappings. We then prove, in a uniformly smooth and uniformly convex Banach space, strong convergence theorems by using a shrinking projection method ...
Kamonrat Nammanee +2 more
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A modification of the forward-backward splitting method for maximal monotone mappings
Numerical Algebra, Control & Optimization, 2013 In this paper, we propose a modification of the forward-backward splitting method for maximal monotone mappings, where we adopt a new step-size scheme in generating the next iterate. This modification is motivated by the ingenious rule proposed by He and Liao in modified Korpelevich's extra-gradient method [13].
Xiao Ding, Deren Han
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