Strong convergence theorems based on a new modified extragradient method for variational inequality problems and fixed point problems in Banach spaces

DOI10.1016/j.camwa.2011.07.056zbMath1231.65112OpenAlexW2012696184MaRDI QIDQ660920

Gang Cai, Shang Quan Bu

Publication date: 5 February 2012

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2011.07.056

zbMATH Keywords

strong convergencefixed pointstrict pseudocontractiongeneral variational inequality

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Variational inequalities (49J40) Iterative procedures involving nonlinear operators (47J25) Linear accretive operators, dissipative operators, etc. (47B44) Numerical methods for variational inequalities and related problems (65K15)

Related Items

The modification of system of variational inequalities for fixed point theory in Banach spaces ⋮ Viscosity iterative algorithm for variational inequality problems and fixed point problems in a real \(q\)-uniformly smooth Banach space ⋮ Strong convergence results for variational inclusions, systems of variational inequalities and fixed point problems using composite viscosity implicit methods ⋮ A simple proof for Imnang's algorithms ⋮ Hybrid extragradient-like viscosity methods for generalized mixed equilibrium problems, variational inclusions, and optimization problems

Cites Work

• Unnamed Item
• Unnamed Item
• Algorithms for approximating minimization problems in Hilbert spaces
• On the convergence of hybrid projection algorithms for asymptotically quasi-\(\phi\)-nonexpansive mappings
• Some new algorithms for solving mixed equilibrium problems
• Approach to common elements of variational inequality problems and fixed point problems via a relaxed extragradient method
• Modified extragradient methods for strict pseudo-contractions and monotone mappings
• Convergence of an iterative algorithm for systems of variational inequalities and nonexpansive mappings with applications
• Approximation of common fixed points for a countable family of relatively nonexpansive mappings in a Banach space and applications
• On viscosity iterative methods for variational inequalities
• Strong convergence theorem by an extragradient method for fixed point problems and variational inequality problems
• On modified iterative method for nonexpansive mappings and monotone mappings
• Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities
• Convergence theorems for \(\lambda \)-strict pseudo-contractions in 2-uniformly smooth Banach spaces
• Approximation of solutions to a system of variational inclusions in Banach spaces
• Modified extragradient methods for a system of variational inequalities in Banach spaces
• Image recovery by convex combinations of sunny nonexpansive retractions
• On Chidume's open questions and approximate solutions of multivalued strongly accretive mapping equations in Banach spaces
• Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals
• Viscosity approximation methods for nonexpansive mappings
• Asymptotic behavior of contractions in Banach spaces
• An explicit projection method for a system of nonlinear variational inequalities with different \((\gamma ,r)\)-cocoercive mappings
• Some new extragradient iterative methods for variational inequalities
• Construction of fixed points of nonlinear mappings in Hilbert space
• Inequalities in Banach spaces with applications
• Strong Convergence of a Proximal-Type Algorithm in a Banach Space
• On iterative methods for solving a system of mixed variational inequalities
• Properties of Fixed-Point Sets of Nonexpansive Mappings in Banach Spaces

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