An iterative algorithm based on M-proximal mappings for a system of generalized implicit variational inclusions in Banach spaces
type: Item
instance of: scholarly article
title: An iterative algorithm based on M-proximal mappings for a system of generalized implicit variational inclusions in Banach spaces
zbMATH Open document ID: 1197.47076
author: M. I. Bhat
author: Naeem Ahmad
author: K. R. Kazmi
published in: Journal of Computational and Applied Mathematics
publication date: 2009-10-09T00:00:00Z
review text: The notion of M-proximal mapping for a nonconvex, proper, lower semicontinuous and subdifferentiable functional on a Banach space is introduced. It is an extension of the P-proximal mappings given by \textit{X.\,P.\thinspace Ding} and \textit{F.\,Q.\thinspace Xia} [J.~Comput.\ Appl.\ Math.\ 147, No.\,2, 369--383 (2002; Zbl 1009.49011)]. Using the concept of M-proximal mapping, an equivalence is established between a system of generalized implicit variational inclusions and a new system of implicit Wiener-Hopf equations. A new iterative algorithm is proposed for a system of generalized implicit variational inclusions. The stability and the convergence of the iterative algorithm are established.
reviewed by: Viorel Arnăutu
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47J22
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 65K10
zbMATH DE Number: 5612607
zbMATH Keywords: generalized implicit variational inclusions
zbMATH Keywords: M-proximal mapping
zbMATH Keywords: implicit Wiener-Hopf equations
zbMATH Keywords: iterative algorithm
zbMATH Keywords: Banach space
zbMATH Keywords: stability
zbMATH Keywords: convergence
MaRDI profile type: Publication
full work available at URL: j.cam.2009.07.028
OpenAlex ID: W2073160011
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DOI: 10.1016/J.CAM.2009.07.028
description: scientific article; zbMATH DE number 5612607