Results 1 to 10 of about 805 (274)
Fixed Point Theory and Applications, 2008 We 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 ...
Cheng Yun, Tian Ming
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Discrete Dynamics in Nature and Society, 2011 We introduce an iterative sequence for finding a common element of the set of fixed points of a nonexpansive mapping and the solutions of the variational inequality problem for three inverse-strongly monotone mappings.
Wiyada Kumam +2 more
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Abstract and Applied Analysis, 2012 We introduce a general implicit iterative scheme base on viscosity approximation method with a ϕ-strongly pseudocontractive mapping for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed ...
Pongsakorn Sunthrayuth, Poom Kumam
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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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Convergence of Iterative Sequences for Fixed Point and Variational Inclusion Problems
Fixed Point Theory and Applications, 2011 An iterative process is considered for finding a common element in the fixed point set of a strict pseudocontraction and in the zero set of a nonlinear mapping which is the sum of a maximal monotone operator and an inverse strongly monotone mapping ...
Yu Li, Liang Ma
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Journal of Inequalities and Applications, 2008 We introduce an iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of a variational inclusion with set-valued maximal monotone mapping and inverse strongly monotone mappings, the set of solutions of ...
Shyu DavidS +3 more
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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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Mathematics, 2019 In this work, we study the inclusion problem of the sum of two monotone operators and the fixed-point problem of nonexpansive mappings in Hilbert spaces. We prove the weak and strong convergence theorems under some weakened conditions.
Prasit Cholamjiak +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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