Hybrid shrinking projection method for a generalized equilibrium problem, a maximal monotone operator and a countable family of relatively nonexpansive mappings

DOI10.1016/j.camwa.2011.02.028zbMath1368.47047OpenAlexW2078074837MaRDI QIDQ639055

Sy-Ming Guu, Lu-Chuan Ceng, Hui-ying Hu, Jen-Chih Yao

Publication date: 18 September 2011

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2011.02.028

zbMATH Keywords

strong convergencemaximal monotone operatorgeneralized equilibrium problemrelatively nonexpansive mappinguniformly smooth and uniformly convex Banach spacehybrid shrinking projection method

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10)

Related Items

Mosco convergence results for common fixed point problems and generalized equilibrium problems in Banach spaces ⋮ Strong convergence theorem for totally quasi-\(\phi\)-asymptotically nonexpansive multi-valued mappings under relaxed conditions ⋮ A shrinking projection method for nonexpansive mappings with nonsummable errors in a Hadamard space ⋮ Convergence of a hybrid iterative scheme for fixed points of nonexpansive maps, solutions of equilibrium, and variational inequalities problems ⋮ Strong convergence theorems of nonlinear operator equations for countable family of multi-valued total quasi-\(\phi\)-asymptotically nonexpansive mappings with applications ⋮ Hybrid shrinking projection extragradient-like algorithms for equilibrium and fixed point problems ⋮ An iterative solution to a system of nonlinear Hammerstein type equations and a system of generalized mixed equilibrium problems ⋮ The approximation of common element for maximal monotone operator, generalized mixed equilibrium problem and fixed point problem ⋮ Hybrid algorithm for generalized mixed equilibrium problems and variational inequality problems and fixed point problems ⋮ A new iterative method for solving a system of generalized mixed equilibrium problems for a countable family of generalized quasi-\(\phi\)-asymptotically nonexpansive mappings ⋮ \(J\)-variational inequalities and zeroes of a family of maximal monotone operators by sunny generalized nonexpansive retraction ⋮ Strong convergence of projection methods for a countable family of nonexpansive mappings and applications to constrained convex minimization problems ⋮ Hybrid methods for solving simultaneously an equilibrium problem and countably many fixed point problems in a Hilbert space ⋮ A relaxed hybrid shrinking iteration approach to solving generalized mixed equilibrium problems for totally quasi-\(\phi\)-asymptotically nonexpansive mappings ⋮ Algorithms for a system of generalized mixed equilibrium problems and a countable family of some nonlinear multi-valued nonexpansive-type maps

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A strong convergence theorem for relatively nonexpansive mappings in a Banach space
• Approximate proximal algorithms for generalized variational inequalities with paramonotonicity and pseudomonotonicity
• Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space
• Generalized implicit hybrid projection-proximal point algorithm for maximal monotone operators in Hilbert space
• New accuracy criteria for modified approximate proximal point algorithms in Hilbert spaces
• On hybrid proximal-type algorithms in Banach spaces
• Strong convergence of an iterative sequence for maximal monotone operators in a Banach space
• Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups.
• Forcing strong convergence of proximal point iterations in a Hilbert space
• Strong convergence theorems for relatively nonexpansive mappings in a Banach space
• An inexact proximal-type algorithm in Banach spaces
• Approximate proximal algorithms for generalized variational inequalities with pseudomonotone multifunctions
• Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces
• On the projection methods for fixed point problems
• On the Convergence of the Proximal Point Algorithm for Convex Minimization
• Monotone Operators and the Proximal Point Algorithm
• Asymptotic Behavior of Relatively Nonexpansive Operators in Banach Spaces
• Iterations of paracontractions and firmaly nonexpansive operators with applications to feasibility and optimization
• Weak Convergence of Orbits of Nonlinear Operators in Reflexive Banach Spaces
• Strong Convergence of a Proximal-Type Algorithm in a Banach Space
• Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
• On the Maximality of Sums of Nonlinear Monotone Operators

This page was built for publication: Hybrid shrinking projection method for a generalized equilibrium problem, a maximal monotone operator and a countable family of relatively nonexpansive mappings