A new iteration method for nonexpansive mappings and monotone mappings in Hilbert spaces

DOI10.1155/2010/251761zbMath1187.47049OpenAlexW1987176269WikidataQ59251438 ScholiaQ59251438MaRDI QIDQ962476

Jong Soo Jung

Publication date: 7 April 2010

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/229592

zbMATH Keywords

strong convergenceHilbert spacenonexpansive mappingsviscosity approximation methodmonotone mappingscomposite iterative scheme

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items

Composite viscosity methods for common solutions of general mixed equilibrium problem, variational inequalities and common fixed points ⋮ General iterative methods for systems of variational inequalities with the constraints of generalized mixed equilibria and fixed point problem of pseudocontractions ⋮ General iterative methods for monotone mappings and pseudocontractive mappings related to optimization problems ⋮ S-iteration process of Halpern-type for common solutions of nonexpansive mappings and monotone variational inequalities ⋮ Composite iterative algorithms for variational inequality and fixed point problems in real smooth and uniformly convex Banach spaces ⋮ A general iterative approach to variational inequality problems and optimization problems ⋮ Some modified extragradient methods for solving split feasibility and fixed point problems ⋮ Weak convergence theorems for strictly pseudocontractive mappings and generalized mixed equilibrium problems ⋮ General iterative algorithms for monotone inclusion, variational inequality and fixed point problems

Cites Work

• Viscosity approximation methods for nonexpansive mappings and monotone mappings
• On the weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in Hilbert space
• Nonlinear complementarity problem and systems of convex inequalities
• Regularization of nonlinear ill-posed variational inequalities and convergence rates
• An iterative approach to quadratic optimization
• Weak convergence theorems for nonexpansive mappings and monotone mappings
• Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings
• Viscosity approximation methods for nonexpansive mappings
• Viscosity approximation methods for fixed-points problems
• Construction of fixed points of nonlinear mappings in Hilbert space
• STRONG CONVERGENCE OF COMPOSITE ITERATIVE METHODS FOR NONEXPANSIVE MAPPINGS
• Monotone Operators and the Proximal Point Algorithm
• Nonlinear monotone operators and convex sets in Banach spaces
• Variational inequalities
• On the Maximality of Sums of Nonlinear Monotone Operators
• Unnamed Item
• Unnamed Item
• Unnamed Item