Generalized nonlinear mixed implicit quasi-variational inclusions with set-valued mappings.
type: Item
instance of: scholarly article
title: Generalized nonlinear mixed implicit quasi-variational inclusions with set-valued mappings.
zbMATH Open document ID: 1034.47032
DOI: 10.1155/S1025583402000425
author: Ravi P. Agarwal
author: Yeol Je Cho
author: Nan-Jing Huang
published in: Journal of Inequalities and Applications
publication date: 2002-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/123405
review text: This article deals with the generalized nonlinear mixed implicit quasi-variational inclusion with set-valued mappings \[ 0\leq N(x,y)+M (w,z),\;x\in Su,\;y\in Tu,\;z\in Gu,\;w\in Pu,\;w\in\text{dom} (M (\cdot,z)), \] where \(G,S,T,P:H\to 2^H\) are set-valued mappings, \(N:H\times H\to H\) a single-valued mapping, \(M:H\times H\to 2^H\) a set-valued mapping such that \(M(\cdot,t): H\to 2^H\) is a maximal monotone mapping and range \((P)\cap\text{dom}(M(\cdot,t)) \neq\emptyset\) \( (t\in H)\) and some its special variants. The problem above is equivalent to the problem \[ w= (I+\rho M ((w-\rho N(x,y) ),z) )^{-1} (w-\rho (N(x,y))) \] with a single-valued operator. For solving this problem, some iterative algorithms are considered. The main results are theorems about the existence of solutions and the convergence of iterations.
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 49J30
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H05
zbMATH DE Number: 1902232
zbMATH Keywords: implicit quasi-variational inclusion
zbMATH Keywords: set-valued mapping
zbMATH Keywords: iterative algorithm
zbMATH Keywords: existence
zbMATH Keywords: convergence
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
OpenAlex ID: W1992077187
description: scientific article; zbMATH DE number 1902232