Viscosity approximation with weak contractions for fixed point problem, equilibrium problem, and variational inequality problem

DOI10.1007/S10483-010-1360-XzbMath1204.41028OpenAlexW1972348240MaRDI QIDQ605256

Shi Sheng Zhang, Heung-Wing Joseph Lee, Chi Kin Chan, Jing Ai Liu

Publication date: 23 November 2010

Published in: Applied Mathematics and Mechanics. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10483-010-1360-x

zbMATH Keywords

minimization problemnonexpansive mappingequilibrium problemimplicit iterationviscosity approximationweak contraction mapping

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (1)

A new modified hybrid steepest-descent by using a viscosity approximation method with a weakly contractive mapping for a system of equilibrium problems and fixed point problems with minimization problems

Cites Work

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• Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings
• Construction of fixed points of nonlinear mappings in Hilbert space
• Hybrid Steepest Descent Method for Variational Inequality Problem over the Fixed Point Set of Certain Quasi-nonexpansive Mappings
• A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces
• Strong convergence to common fixed points of infinite nonexpansive mappings and applications

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