\(H(\cdot ,\cdot)\)-cocoercive operator and an application for solving generalized variational inclusions
type: Item
instance of: scholarly article
title: \(H(\cdot ,\cdot)\)-cocoercive operator and an application for solving generalized variational inclusions
zbMATH Open document ID: 1301.47068
DOI: 10.1155/2011/261534
author: Rais Ahmad
author: M. M. Wong
author: Mohd Dilshad
author: Jen-Chih Yao
published in: Abstract and Applied Analysis
publication date: 2011-09-09T00:00:00Z
review text: Summary: The purpose of this paper is to introduce a new \(H(\cdot, \cdot)\)-cocoercive operator, which generalizes many existing monotone operators. The resolvent operator associated with the \(H(\cdot ,\cdot)\)-cocoercive operator is defined, and its Lipschitz continuity is proved. By using techniques of resolvent operator, a new iterative algorithm for solving generalized variational inclusions is constructed. Under some suitable conditions, we prove the convergence of iterative sequences generated by the algorithm. For illustration, some examples are given.
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 47J22
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 5946500
Wikidata QID: Q58654103
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/261534
OpenAlex ID: W1974923413
cites work: Further applications of a splitting algorithm to decomposition in variational inequalities and convex programming
cites work: Co-Coercivity and Its Role in the Convergence of Iterative Schemes for Solving Variational Inequalities
cites work: \(H\)-monotone operator and resolvent operator technique for variational inclusions
cites work: \(H\)-accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces.
cites work: A new system of variational inclusions with \((H,\eta)\)-monotone operators in Hilbert spaces
cites work: Nonlinear relaxed cocoercive variational inclusions involving \((A,\eta)\)-accretive mappings in Banach spaces
cites work: \(H(\cdot ,\cdot )\)-accretive operator with an application for solving variational inclusions in Banach spaces
cites work: Q3161380
cites work: A new class of generalized set-valued implicit variational inclusions in Banach spaces with an application
description: scientific article; zbMATH DE number 5946500