Implicit iterative algorithms for asymptotically nonexpansive mappings in the intermediate sense and Lipschitz-continuous monotone mappings

DOI10.1016/j.cam.2009.11.035zbMath1188.65076OpenAlexW2022523971MaRDI QIDQ848545

Jen-Chih Yao, Lu-Chuan Ceng, Daya Ram Sahu

Publication date: 4 March 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2009.11.035

zbMATH Keywords

fixed pointsvariational inequalitiesweak convergenceHilbert spaceiterative algorithmsapproximationasymptotically nonexpansive mappingOpial's conditionmonotone mappingdemiclosedness principle

Mathematics Subject Classification ID

Variational inequalities (49J40) Iterative procedures involving nonlinear operators (47J25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Numerical solutions to equations with nonlinear operators (65J15) Existence theories for problems in abstract spaces (49J27) Numerical methods for variational inequalities and related problems (65K15)

Related Items

Strong convergence theorem for the modified generalized equilibrium problem and fixed point problem of strictly pseudo-contractive mappings ⋮ Strong convergence theorems by a hybrid extragradient-like approximation method for asymptotically nonexpansive mappings in the intermediate sense in Hilbert spaces ⋮ Total asymptotically nonexpansive mappings and generalized variational-like inclusion problems in semi-inner product spaces ⋮ Weak and strong convergence theorems for asymptotically pseudo-contraction mappings in the intermediate sense in Hilbert spaces ⋮ A shrinking projection method for generalized mixed equilibrium problems, variational inclusion problems and a finite family of quasi-nonexpansive mappings ⋮ Modified block iterative algorithm for solving convex feasibility problems in Banach spaces ⋮ New iterative schemes for asymptotically quasi-nonexpansive mappings ⋮ On the convergence of implicit iterative processes for asymptotically pseudocontractive mappings in the intermediate sense ⋮ An implicit hierarchical fixed-point approach to general variational inequalities in Hilbert spaces ⋮ Approximating the common fixed points of two sequences of uniformly quasi-Lipschitzian mappings in convex metric spaces ⋮ Strong convergence of approximated iterations for asymptotically pseudocontractive mappings ⋮ Convergence of three-step iterations for nearly asymptotically nonexpansive mappings in \(\operatorname{CAT}(k)\) spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An approximate proximal-extragradient type method for monotone variational inequalities
• Strong convergence theorem by an extragradient method for fixed point problems and variational inequality problems
• On the convergence analysis of inexact hybrid extragradient proximal point algorithms for maximal monotone operators
• 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
• Asymptotically strict pseudocontractive mappings in the intermediate sense
• Regularization of nonlinear ill-posed variational inequalities and convergence rates
• Convergence rate analysis of iteractive algorithms for solving variational inequality problems
• Weak convergence theorems for nonexpansive mappings and monotone mappings
• Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups.
• An extragradient-like approximation method for variational inequality problems and fixed point problems
• Convergence of hybrid steepest-descent methods for generalized variational inequalities
• Approximate proximal algorithms for generalized variational inequalities with pseudomonotone multifunctions
• Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups
• Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings
• Construction of fixed points of nonlinear mappings in Hilbert space
• An Inexact Hybrid Generalized Proximal Point Algorithm and Some New Results on the Theory of Bregman Functions
• Monotone Operators and the Proximal Point Algorithm
• An Outer Approximation Method for the Variational Inequality Problem
• Strong Convergence Theorem by a Hybrid Method for Nonexpansive Mappings and Lipschitz-Continuous Monotone Mappings
• On the Maximality of Sums of Nonlinear Monotone Operators
• A Fixed Point Theorem for Asymptotically Nonexpansive Mappings

This page was built for publication: Implicit iterative algorithms for asymptotically nonexpansive mappings in the intermediate sense and Lipschitz-continuous monotone mappings