A viscosity extragradient method for an equilibrium problem and fixed point problem in Hilbert space
type: Item
instance of: scholarly article
title: A viscosity extragradient method for an equilibrium problem and fixed point problem in Hilbert space
zbMATH Open document ID: 1421.47003
author: Meiling Zhao
author: Poom Kumam
author: Yeol Je Cho
author: Shenghua Wang
published in: Journal of Fixed Point Theory and Applications
publication date: 2018-04-11T00:00:00Z
review text: Let \(H\) be a real Hilbert space and \(C\) be its nonempty, closed and convex subset. Let \(T:C\to C\) be a nonexpansive mapping and \(f:C\times C\to \mathbb{R}\) be a function satisfying the following conditions: (1)~\(f\) is pseudomonotone and \(f(x,x)=0\) for each \(x\in C\); (2)~\(f\) is Lipschitz-type continuous on~\(C\); (3)~\(f(x,\cdot)\) is convex and subdifferentiable, for each \(x\in C\); (4)~\(f(x,y)\) is jointly weakly continuous on \(C\times C\). Assume that \(A=\operatorname{Fix}(T)\cap EP(f)\neq\emptyset\), where \(\operatorname{Fix}(T)\) is the set of fixed points of \(T\) and \(EP(f)=\{z\in C:f(z,y)\geq0\text{ for all }y\in C\}\) is the set of solutions of the equilibrium problem of~\(f\). The authors present an algorithm to find an element in \(A\). A numerical example illustrates the algorithm.
reviewed by: Zoran Kadelburg
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 6858711
zbMATH Keywords: equilibrium problem
zbMATH Keywords: pseudomonotone equilibrium problem
zbMATH Keywords: fixed point
zbMATH Keywords: Hilbert space
MaRDI profile type: Publication
full work available at URL: s11784-018-0512-y
OpenAlex ID: W2792962879
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DOI: 10.1007/S11784-018-0512-Y
description: scientific article; zbMATH DE number 6858711