Convergence theorems for maximal monotone operators, weak relatively nonexpansive mappings and equilibrium problems
type: Item
instance of: scholarly article
title: Convergence theorems for maximal monotone operators, weak relatively nonexpansive mappings and equilibrium problems
zbMATH Open document ID: 1323.47074
DOI: 10.1155/2012/804538
author: K. Nammanee
author: Suthep Suantai
author: Prasit Cholamjiak
published in: Journal of Applied Mathematics
publication date: 2012-11-15T00:00:00Z
review text: Summary: We introduce hybrid-iterative schemes for solving a system of the zero-finding problems of maximal monotone operators, the equilibrium problem, and the fixed point problem of weak relatively nonexpansive mappings. We then prove, in a uniformly smooth and uniformly convex Banach space, strong convergence theorems by using a shrinking projection method. We finally apply the obtained results to a system of convex minimization problems.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H05
zbMATH DE Number: 6106313
zbMATH Keywords: strong convergence
zbMATH Keywords: shrinking projection method
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/804538
OpenAlex ID: W2044373678
Wikidata QID: Q58907378
cites work: Composite iterative schemes for maximal monotone operators in reflexive Banach spaces
cites work: Approximate proximal point algorithms for finding zeroes of maximal monotone operators in Hilbert spaces
cites work: Iterative approaches to find zeros of maximal monotone operators by hybrid approximate proximal point methods
cites work: On the Convergence of the Proximal Point Algorithm for Convex Minimization
cites work: Strong convergence of an iterative sequence for maximal monotone operators in a Banach space
cites work: Convergence of generalized proximal point algorithms
cites work: A new iterative scheme for equilibrium problems, fixed point problems for nonexpansive mappings and maximal monotone operators
cites work: Approximating zeros of monotone operators by proximal point algorithms
cites work: A hybrid iterative scheme for a maximal monotone operator and two countable families of relatively quasi-nonexpansive mappings for generalized mixed equilibrium and variational inequality problems
cites work: A system of generalized mixed equilibrium problems, maximal monotone operators, and fixed point problems with application to optimization problems
cites work: Hybrid proximal-point methods for zeros of maximal monotone operators, variational inequalities and mixed equilibrium problems
cites work: Q4910093
cites work: A new iterative scheme for generalized mixed equilibrium, variational inequality problems, and a zero point of maximal monotone operators
cites work: Convergence of an iterative algorithm for common solutions for zeros of maximal accretive operator with applications
cites work: On convergence criteria of generalized proximal point algorithms
cites work: Strong convergence of a proximal point algorithm with general errors
cites work: Q5618030
cites work: Monotone Operators and the Proximal Point Algorithm
cites work: Approximating solutions of maximal monotone operators in Hilbert spaces
cites work: Weak and strong convergence theorems for maximal monotone operators in a Banach space
cites work: Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings
cites work: Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces
cites work: A hybrid iterative scheme for equilibrium problems, variational inequality problems, and fixed point problems in Banach spaces
cites work: Convergence analysis for a system of equilibrium problems and a countable family of relatively quasi-nonexpansive mappings in Banach spaces
cites work: A hybrid method for a countable family of multivalued maps, equilibrium problems, and variational inequality problems
cites work: Q3173960
cites work: A hybrid approximation method for equilibrium and fixed point problems for a monotone mapping and a nonexpansive mapping
cites work: A new hybrid iterative method for solution of equilibrium problems and fixed point problems for an inverse strongly monotone operator and a nonexpansive mapping
cites work: Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces
cites work: Iterative approximation method for finite family of relatively quasi nonexpansive mappings and systems of equilibrium problems
cites work: A new hybrid iterative scheme for countable families of relatively quasi-nonexpansive mappings and system of equilibrium problems
cites work: Nonlinear functional analysis. Fixed point theory and its applications
cites work: Asymptotic Behavior of Relatively Nonexpansive Operators in Banach Spaces
cites work: Weak Convergence of Orbits of Nonlinear Operators in Reflexive Banach Spaces
cites work: Strong convergence theorems for monotone mappings and relatively weak nonexpansive mappings
cites work: Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications
cites work: Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
cites work: Strong Convergence of a Proximal-Type Algorithm in a Banach Space
cites work: A strong convergence theorem for relatively nonexpansive mappings in a Banach space
cites work: Q4366516
cites work: Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces
cites work: Existence and Approximation of Fixed Points of Firmly Nonexpansive-Type Mappings in Banach Spaces
cites work: Characterization of the subdifferentials of convex functions
cites work: On the maximal monotonicity of subdifferential mappings
description: scientific article; zbMATH DE number 6106313