A new iterative algorithm of pseudomonotone mappings for equilibrium problems in Hilbert spaces

DOI10.1186/1029-242X-2013-128zbMath1455.47022WikidataQ59293347 ScholiaQ59293347MaRDI QIDQ2636680

Jong Kyu Kim, Won Hee Lim

Publication date: 31 January 2014

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

zbMATH Keywords

fixed pointsstrong convergenceequilibrium problemextragradient methodsstrict pseudocontractionpseudomonotone mappingfixed point iteration methodsLipschitz-type continuous mapping

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Iterative procedures involving nonlinear operators (47J25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

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Cites Work

• Convergence theorem for fixed points of nearly uniformly \(L\)-Lipschitzian asymptotically generalized \(\Phi \)-hemicontractive mappings
• Convergence theorems of implicit iterative sequences for a finite family of asymptotically quasi-nonexpansive type mappings
• New iterative scheme with nonexpansive mappings for equilibrium problems and variational inequality problems in Hilbert spaces
• Iterative algorithms for mixed equilibrium problems, strict pseudocontractions and monotone mappings
• Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces
• Approximating solutions of variational inequalities for asymptotically nonexpansive mappings
• Characterization of generalized monotone maps
• Weak convergence theorems for nonexpansive mappings and monotone mappings
• Iterative methods for strict pseudo-contractions in Hilbert spaces
• Strong convergence of the CQ method for fixed point iteration processes
• Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings

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