Hybrid proximal-point methods for common solutions of equilibrium problems and zeros of maximal monotone operators
type: Item
instance of: scholarly article
title: Hybrid proximal-point methods for common solutions of equilibrium problems and zeros of maximal monotone operators
zbMATH Open document ID: 1180.90334
author: Jen-Chih Yao
author: L. C. Ceng
author: Giandomenico Mastroeni
published in: Journal of Optimization Theory and Applications
publication date: 2009-11-04T00:00:00Z
review text: The authors consider the problem of finding common solution points of an equilibrium problem with a monotone bi-function and a multi-valued inclusion with monotone mapping in a Banach space. Thus, it is an extension of the problem from the paper by \textit{W. Takahashi} and \textit{K. Zembayashi} [Nonlinear Anal., Theory Methods Appl. 70, No. 1 (A), 45--57 (2009; Zbl 1170.47049)] where a fixed point problem of a non-expansive mapping was used instead of the multi-valued inclusion. In the latter paper, two hybrid proximal point type methods were proposed and their strong and weak convergence was established. The authors adjust those methods to the problem under solution and also prove their strong and weak convergence.
reviewed by: Igor V. Konnov
Mathematics Subject Classification ID: 90C33
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47J22
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 65K15
zbMATH DE Number: 5625128
zbMATH Keywords: equilibrium problems
zbMATH Keywords: multi-valued inclusions
zbMATH Keywords: monotone mappings
zbMATH Keywords: common solutions
zbMATH Keywords: Banach spaces
zbMATH Keywords: hybrid proximal point type methods
zbMATH Keywords: strong convergence
zbMATH Keywords: weak convergence
MaRDI profile type: Publication
full work available at URL: s10957-009-9538-z
OpenAlex ID: W2075317557
cites work: Q5618030
cites work: Monotone Operators and the Proximal Point Algorithm
cites work: A hybrid iterative scheme for mixed equilibrium problems and fixed point problems
cites work: An inexact proximal-type algorithm in Banach spaces
cites work: Strong convergence of an iterative sequence for maximal monotone operators in a Banach space
cites work: Weak and strong convergence theorems for maximal monotone operators in a Banach space
cites work: Modified proximal-point algorithm for maximal monotone operators in Banach spaces
cites work: On the Convergence of the Proximal Point Algorithm for Convex Minimization
cites work: Q4366516
cites work: Q4681445
cites work: Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces
cites work: Hybrid viscosity approximation schemes for equilibrium problems and fixed point problems of infinitely many nonexpansive mappings
cites work: Q3999276
cites work: Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
cites work: On the projection methods for fixed point problems
cites work: Q4894797
cites work: Strong Convergence of a Proximal-Type Algorithm in a Banach Space
cites work: Inequalities in Banach spaces with applications
cites work: Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process
DOI: 10.1007/S10957-009-9538-Z
description: scientific article; zbMATH DE number 5625128