Finding common solutions of a variational inequality, a general system of variational inequalities, and a fixed-point problem via a hybrid extragradient method

DOI10.1155/2011/626159zbMath1222.49010OpenAlexW4299508591WikidataQ59253427 ScholiaQ59253427MaRDI QIDQ623561

Lu-Chuan Ceng, Sy-Ming Guu, Jen-Chih Yao

Publication date: 8 February 2011

Published in: Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/232955

zbMATH Keywords

variational inequalityfixed point theoremviscosity approximation methodMann-type iteration methodhybrid extragradient method

Mathematics Subject Classification ID

Variational inequalities (49J40) Iterative procedures involving nonlinear operators (47J25) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

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Cites Work

• Convergence of hybrid steepest-descent methods for variational inequalities
• Approach to common elements of variational inequality problems and fixed point problems via a relaxed extragradient method
• Iterative algorithm for completely generalized set-valued strongly nonlinear mixed variational-like inequalities
• Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces
• 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
• Mixed projection methods for systems of variational inequalities
• An implicit iterative scheme for monotone variational inequalities and fixed point problems
• Convergence analysis of modified hybrid steepest-descent methods with variable parameters for variational inequalities
• On generalized variational-like inequalities with generalized monotone multivalued mappings
• An interior point method with Bregman functions for the variational inequality problem with paramonotone operators
• Regularization of nonlinear ill-posed variational inequalities and convergence rates
• Iterative algorithms for finding approximate solutions for general strongly nonlinear variational inequalities
• Weak convergence theorems for nonexpansive mappings and monotone mappings
• Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals
• Some developments in general variational inequalities
• Iterative algorithm for finding approximate solutions to completely generalized strongly nonlinear quasivariational inequalities
• Iterative methods for strict pseudo-contractions in Hilbert spaces
• An extragradient-like approximation method for variational inequality problems and fixed point problems
• Convergence of hybrid steepest-descent methods for generalized variational inequalities
• Iterative algorithm for generalized set-valued strongly nonlinear mixed variational-like inequali\-ties
• Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings
• Construction of fixed points of nonlinear mappings in Hilbert space
• Variational Inequalities with Generalized Monotone Operators
• Strong Convergence Theorem by a Hybrid Method for Nonexpansive Mappings and Lipschitz-Continuous Monotone Mappings