Hybrid extragradient methods for asymptotically strict pseudo-contractions in the intermediate sense and variational inequality problems

DOI10.1080/02331934.2010.527340zbMath1368.47061OpenAlexW2077227386MaRDI QIDQ3093096

Shuechin Huang

Publication date: 12 October 2011

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331934.2010.527340

zbMATH Keywords

strong convergenceweak convergencevariational inequalityMann iterationinverse-strongly monotone mappingmonotone mappingdemiclosedness principlehybrid extragradient methodasymptotically strict pseudo-contraction in the intermediate senseasymptotically strict pseudo-contraction

Mathematics Subject Classification ID

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

Related Items (9)

Fixed point theorems for mappings with condition (B) ⋮ Hybrid iterative method for systems of generalized equilibria with constraints of variational inclusion and fixed point problems ⋮ Weak and strong convergence theorems for asymptotically pseudo-contraction mappings in the intermediate sense in Hilbert spaces ⋮ Generalized mixed equilibria, variational inclusions, and fixed point problems ⋮ Hybrid extragradient method with regularization for convex minimization, generalized mixed equilibrium, variational inequality and fixed point problems ⋮ Strong and weak convergence criteria of composite iterative algorithms for systems of generalized equilibria ⋮ Multistep hybrid iterations for systems of generalized equilibria with constraints of several problems ⋮ Convex minimization with constraints of systems of variational inequalities, mixed equilibrium, variational inequality, and fixed point problems ⋮ On a finite family of variational inclusions with the constraints of generalized mixed equilibrium and fixed point problems

Cites Work

• Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces
• Asymptotically strict pseudocontractive mappings in the intermediate sense
• Strong convergence theorems by hybrid method for asymptotically \(k\)-strict pseudo-contractive mapping in Hilbert space
• Regularization of nonlinear ill-posed variational inequalities and convergence rates
• Weak convergence theorems for nonexpansive mappings and monotone mappings
• Mann and Ishikawa iterations with errors for non-Lipschitzian mappings in Banach spaces
• Fixed point solutions of variational inequalities for a finite family of asymptotically nonexpansive mappings without common fixed point assumption
• Convergence of the modified Mann's iteration method for asymptotically strict pseudo-contractions
• Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings
• Construction of fixed points of nonlinear mappings in Hilbert space
• Convergence Theorems for Mappings Which Are Asymptotically Nonexpansive in the Intermediate Sense
• Weak and strong convergence to fixed points of asymptotically nonexpansive mappings
• Modification of the extra-gradient method for solving variational inequalities and certain optimization problems
• Variational Inequalities with Generalized Monotone Operators
• Mann-Type Steepest-Descent and Modified Hybrid Steepest-Descent Methods for Variational Inequalities in Banach Spaces
• A linear operator and associated families of meromorphically multivalent functions

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