A viscosity hybrid steepest descent method for generalized mixed equilibrium problems and variational inequalities for relaxed cocoercive mapping in Hilbert spaces
type: Item
instance of: scholarly article
title: A viscosity hybrid steepest descent method for generalized mixed equilibrium problems and variational inequalities for relaxed cocoercive mapping in Hilbert spaces
zbMATH Open document ID: 1206.47067
DOI: 10.1155/2010/390972
author: Wanpen Chantarangsi
author: Chaichana Jaiboon
author: Poom Kumam
published in: Abstract and Applied Analysis
publication date: 2010-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/226684
review text: Summary: We present an iterative method for fixed point problems, generalized mixed equilibrium problems, and variational inequality problems. Our method is based on the so-called viscosity hybrid steepest descent method. Using this method, we can find the common element of the set of fixed points of a nonexpansive mapping, the set of solutions of generalized mixed equilibrium problems, and the set of solutions of variational inequality problems for a relaxed cocoercive mapping in a real Hilbert space. Then, we prove the strong convergence of the proposed iterative scheme to the unique solution of variational inequality. The results presented in this paper generalize and extend some well-known strong convergence theorems in the literature.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 5791619
zbMATH Keywords: viscosity hybrid steepest descent method
zbMATH Keywords: nonexpansive mapping
zbMATH Keywords: relaxed cocoercive mapping
zbMATH Keywords: real Hilbert space
zbMATH Keywords: strong convergence
Wikidata QID: Q58649840
MaRDI profile type: Publication
OpenAlex ID: W2124505441
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description: scientific article; zbMATH DE number 5791619